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class="vector-toc-numb">2</span> <span>Normalized notation</span> </div> </a> <ul id="toc-Normalized_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Engineering_notation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Engineering_notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Engineering notation</span> </div> </a> <ul id="toc-Engineering_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Significant_figures" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Significant_figures"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Significant figures</span> </div> </a> <button aria-controls="toc-Significant_figures-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Significant figures subsection</span> </button> <ul id="toc-Significant_figures-sublist" class="vector-toc-list"> <li id="toc-Estimated_final_digits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Estimated_final_digits"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Estimated final digits</span> </div> </a> <ul id="toc-Estimated_final_digits-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-E_notation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#E_notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>E notation</span> </div> </a> <ul id="toc-E_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Use_of_spaces" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Use_of_spaces"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Use of spaces</span> </div> </a> <ul id="toc-Use_of_spaces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_examples_of_scientific_notation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_examples_of_scientific_notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further examples of scientific notation</span> </div> </a> <ul id="toc-Further_examples_of_scientific_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Converting_numbers" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Converting_numbers"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Converting numbers</span> </div> </a> <button aria-controls="toc-Converting_numbers-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Converting numbers subsection</span> </button> <ul id="toc-Converting_numbers-sublist" class="vector-toc-list"> <li id="toc-Decimal_to_scientific" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Decimal_to_scientific"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Decimal to scientific</span> </div> </a> <ul id="toc-Decimal_to_scientific-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Scientific_to_decimal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Scientific_to_decimal"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Scientific to decimal</span> </div> </a> <ul id="toc-Scientific_to_decimal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exponential" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exponential"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Exponential</span> </div> </a> <ul id="toc-Exponential-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Basic_operations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Basic_operations"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Basic operations</span> </div> </a> <ul id="toc-Basic_operations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_bases" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_bases"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Other bases</span> </div> </a> <ul id="toc-Other_bases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Scientific notation</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 44 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-44" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">44 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Wetenskaplike_notasie" title="Wetenskaplike notasie – Afrikaans" lang="af" hreflang="af" data-title="Wetenskaplike notasie" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D8%AA%D8%A7%D8%A8%D8%A9_%D8%B9%D9%84%D9%85%D9%8A%D8%A9" title="كتابة علمية – Arabic" lang="ar" hreflang="ar" data-title="كتابة علمية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%88%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8%E0%A6%BF%E0%A6%95_%E0%A6%85%E0%A6%99%E0%A7%8D%E0%A6%95%E0%A6%AA%E0%A6%BE%E0%A6%A4%E0%A6%A8" title="বৈজ্ঞানিক অঙ্কপাতন – Bangla" lang="bn" hreflang="bn" data-title="বৈজ্ঞানিক অঙ্কপাতন" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%AD%D0%BA%D1%81%D0%BF%D0%B0%D0%BD%D1%8D%D0%BD%D1%82%D0%B0%D0%B2%D0%B0%D1%8F_%D0%BD%D0%B0%D1%82%D0%B0%D1%86%D1%8B%D1%8F" title="Экспанэнтавая натацыя – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Экспанэнтавая натацыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%B5%D0%BD_%D0%B7%D0%B0%D0%BF%D0%B8%D1%81" title="Експоненциален запис – Bulgarian" lang="bg" hreflang="bg" data-title="Експоненциален запис" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Notaci%C3%B3_cient%C3%ADfica" title="Notació científica – Catalan" lang="ca" hreflang="ca" data-title="Notació científica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/V%C4%9Bdeck%C3%BD_z%C3%A1pis_%C4%8D%C3%ADsel" title="Vědecký zápis čísel – Czech" lang="cs" hreflang="cs" data-title="Vědecký zápis čísel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Videnskabelig_notation" title="Videnskabelig notation – Danish" lang="da" hreflang="da" data-title="Videnskabelig notation" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Wissenschaftliche_Notation" title="Wissenschaftliche Notation – German" lang="de" hreflang="de" data-title="Wissenschaftliche Notation" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arvu_standardkuju" title="Arvu standardkuju – Estonian" lang="et" hreflang="et" data-title="Arvu standardkuju" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%B9%CF%83%CF%84%CE%B7%CE%BC%CE%BF%CE%BD%CE%B9%CE%BA%CE%AE_%CF%83%CE%B7%CE%BC%CE%B5%CE%B9%CE%BF%CE%B3%CF%81%CE%B1%CF%86%CE%AF%CE%B1" title="Επιστημονική σημειογραφία – Greek" lang="el" hreflang="el" data-title="Επιστημονική σημειογραφία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Notaci%C3%B3n_cient%C3%ADfica" title="Notación científica – Spanish" lang="es" hreflang="es" data-title="Notación científica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Notazio_zientifiko" title="Notazio zientifiko – Basque" lang="eu" hreflang="eu" data-title="Notazio zientifiko" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D9%85%D8%A7%D8%AF_%D8%B9%D9%84%D9%85%DB%8C" title="نماد علمی – Persian" lang="fa" hreflang="fa" data-title="نماد علمی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Notation_scientifique" title="Notation scientifique – French" lang="fr" hreflang="fr" data-title="Notation scientifique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Notaci%C3%B3n_cient%C3%ADfica" title="Notación científica – Galician" lang="gl" hreflang="gl" data-title="Notación científica" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%BC%ED%95%99%EC%A0%81_%EA%B8%B0%EC%88%98%EB%B2%95" title="과학적 기수법 – Korean" lang="ko" hreflang="ko" data-title="과학적 기수법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Notasi_ilmiah" title="Notasi ilmiah – Indonesian" lang="id" hreflang="id" data-title="Notasi ilmiah" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sta%C3%B0alform" title="Staðalform – Icelandic" lang="is" hreflang="is" data-title="Staðalform" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Notazione_scientifica" title="Notazione scientifica – Italian" lang="it" hreflang="it" data-title="Notazione scientifica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9B%D7%AA%D7%99%D7%91_%D7%9E%D7%93%D7%A2%D7%99" title="כתיב מדעי – Hebrew" lang="he" hreflang="he" data-title="כתיב מדעי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Notasyon_syantifik" title="Notasyon syantifik – Haitian Creole" lang="ht" hreflang="ht" data-title="Notasyon syantifik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Zin%C4%81tniskais_pieraksts" title="Zinātniskais pieraksts – Latvian" lang="lv" hreflang="lv" data-title="Zinātniskais pieraksts" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Standartin%C4%97_skai%C4%8Diaus_i%C5%A1rai%C5%A1ka" title="Standartinė skaičiaus išraiška – Lithuanian" lang="lt" hreflang="lt" data-title="Standartinė skaičiaus išraiška" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Norm%C3%A1lalak" title="Normálalak – Hungarian" lang="hu" hreflang="hu" data-title="Normálalak" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wetenschappelijke_notatie" title="Wetenschappelijke notatie – Dutch" lang="nl" hreflang="nl" data-title="Wetenschappelijke notatie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%8C%87%E6%95%B0%E8%A1%A8%E8%A8%98" title="指数表記 – Japanese" lang="ja" hreflang="ja" data-title="指数表記" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Vitenskapelig_notasjon" title="Vitenskapelig notasjon – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Vitenskapelig notasjon" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Notacja_naukowa" title="Notacja naukowa – Polish" lang="pl" hreflang="pl" data-title="Notacja naukowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://pt.wikipedia.org/wiki/Nota%C3%A7%C3%A3o_cient%C3%ADfica" title="Notação científica – Portuguese" lang="pt" hreflang="pt" data-title="Notação científica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BA%D1%81%D0%BF%D0%BE%D0%BD%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B7%D0%B0%D0%BF%D0%B8%D1%81%D1%8C" title="Экспоненциальная запись – Russian" lang="ru" hreflang="ru" data-title="Экспоненциальная запись" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%AD%E0%B7%8A%E0%B6%B8%E0%B6%9A_%E0%B6%85%E0%B6%82%E0%B6%9A%E0%B6%B1%E0%B6%BA" title="විද්‍යාත්මක අංකනය – Sinhala" lang="si" hreflang="si" data-title="විද්‍යාත්මක අංකනය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Scientific_notation" title="Scientific notation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Scientific notation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Znanstveni_zapis" title="Znanstveni zapis – Slovenian" lang="sl" hreflang="sl" data-title="Znanstveni zapis" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Qormo_saynis" title="Qormo saynis – Somali" lang="so" hreflang="so" data-title="Qormo saynis" 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class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Concise notation for large or small numbers</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about a numeric notation. For the musical notation, see <a href="/wiki/Scientific_pitch_notation" title="Scientific pitch notation">Scientific pitch notation</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"E notation" redirects here. For the series of preferred numbers, see <a href="/wiki/E_series_of_preferred_numbers" title="E series of preferred numbers">E series</a>. For the food additive codes, see <a href="/wiki/E_number" title="E number">E number</a>.</div> <p class="mw-empty-elt"> </p><p><b>Scientific notation</b> is a way of expressing <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">numbers</a> that are too large or too small to be conveniently written in <a href="/wiki/Decimal_form" class="mw-redirect" title="Decimal form">decimal form</a>, since to do so would require writing out an inconveniently long string of digits. It may be referred to as <b>scientific form</b> or <b>standard index form</b>, or <b>standard form</b> in the United Kingdom. This <a href="/wiki/Base_ten" class="mw-redirect" title="Base ten">base ten</a> notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain <a href="/wiki/Arithmetic_operations" class="mw-redirect" title="Arithmetic operations">arithmetic operations</a>. On <a href="/wiki/Scientific_calculators" class="mw-redirect" title="Scientific calculators">scientific calculators</a>, it is usually known as "SCI" display mode. </p> <table class="wikitable" style="float:right; margin:5px;"> <tbody><tr> <th>Decimal notation </th> <th>Scientific notation </th></tr> <tr> <td><span class="nowrap"><span data-sort-value="7000200000000000000♠"></span>2</span> </td> <td><span class="nowrap"><span data-sort-value="7000200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>0</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7002300000000000000♠"></span>300</span> </td> <td><span class="nowrap"><span data-sort-value="7002300000000000000♠"></span>3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7003432176800000000♠"></span>4<span style="margin-left:.25em;">321</span>.768</span> </td> <td><span class="nowrap"><span data-sort-value="7003432176800000000♠"></span>4.321<span style="margin-left:.25em;">768</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>3</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="2995470000000000000♠"></span>−53<span style="margin-left:.25em;">000</span></span> </td> <td><span class="nowrap"><span data-sort-value="2995470000000000000♠"></span>−5.3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>4</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7009672000000000000♠"></span>6<span style="margin-left:.25em;">720</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span></span> </td> <td><span class="nowrap"><span data-sort-value="7009672000000000000♠"></span>6.72<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>9</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="6999200000000000000♠"></span>0.2</span> </td> <td><span class="nowrap"><span data-sort-value="6999200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−1</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7002987000000000000♠"></span>987</span> </td> <td><span class="nowrap"><span data-sort-value="7002986999999999999♠"></span>9.87<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="6991751000000000000♠"></span>0.000<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">007</span><span style="margin-left:.25em;">51</span></span> </td> <td><span class="nowrap"><span data-sort-value="6991751000000000000♠"></span>7.51<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−9</sup></span> </td></tr></tbody></table> <p>In scientific notation, nonzero numbers are written in the form </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent" style="padding-left: 1.5em;"><i>m</i> × 10<sup><i>n</i></sup></div> <p>or <i>m</i> times ten raised to the power of <i>n</i>, where <i>n</i> is an <a href="/wiki/Integer" title="Integer">integer</a>, and the <a href="/wiki/Coefficient" title="Coefficient">coefficient</a> <i>m</i> is a nonzero <a href="/wiki/Real_number" title="Real number">real number</a> (usually between 1 and 10 in absolute value, and nearly always written as a <a href="/wiki/Decimal" title="Decimal">terminating decimal</a>). The integer <i>n</i> is called the <a href="/wiki/Exponent" class="mw-redirect" title="Exponent">exponent</a> and the real number <i>m</i> is called the <i><a href="/wiki/Significand" title="Significand">significand</a></i> or <i>mantissa</i>.<sup id="cite_ref-Calio_2017_1-0" class="reference"><a href="#cite_note-Calio_2017-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the <a href="/wiki/Fractional_part" title="Fractional part">fractional part</a> of the <a href="/wiki/Common_logarithm" title="Common logarithm">common logarithm</a>. If the number is negative then a minus sign precedes <i>m</i>, as in ordinary decimal notation. In <a href="#Normalized_notation">normalized notation</a>, the exponent is chosen so that the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> (modulus) of the significand <i>m</i> is at least 1 but less than 10. </p><p><a href="/wiki/Decimal_floating_point" title="Decimal floating point">Decimal floating point</a> is a computer arithmetic system closely related to scientific notation. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For the history of exponential notation, see <a href="/wiki/Exponentiation#20th_century" title="Exponentiation">Exponentiation § 20th century</a>.</div> <div class="mw-heading mw-heading2"><h2 id="Normalized_notation">Normalized notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=2" title="Edit section: Normalized notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Normalized_number" title="Normalized number">Normalized number</a></div> <p>Any real number can be written in the form <span style="white-space:nowrap"><i>m</i><span style="margin-left:0.27em;margin-right:0.27em">×</span>10<span style="display:none">^</span><sup><i>n</i></sup></span> in many ways: for example, 350 can be written as <span class="nowrap"><span data-sort-value="7002350000000000000♠"></span>3.5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span> or <span class="nowrap"><span data-sort-value="7002350000000000000♠"></span>35<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>1</sup></span> or <span class="nowrap"><span data-sort-value="7002350000000000000♠"></span>350<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>0</sup></span>. </p><p>In <i>normalized</i> scientific notation (called "standard form" in the United Kingdom), the exponent <i>n</i> is chosen so that the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> of <i>m</i> remains at least one but less than ten (<span class="nowrap">1 ≤ |<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"><i>m</i></span>| < 10</span>). Thus 350 is written as <span class="nowrap"><span data-sort-value="7002350000000000000♠"></span>3.5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span>. This form allows easy comparison of numbers: numbers with bigger exponents are (due to the normalization) larger than those with smaller exponents, and subtraction of exponents gives an estimate of the number of <a href="/wiki/Orders_of_magnitude" class="mw-redirect" title="Orders of magnitude">orders of magnitude</a> separating the numbers. It is also the form that is required when using tables of <a href="/wiki/Common_logarithm" title="Common logarithm">common logarithms</a>. In normalized notation, the exponent <i>n</i> is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as <span class="nowrap"><span data-sort-value="6999500000000000000♠"></span>5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−1</sup></span>). The 10 and exponent are often omitted when the exponent is 0. For a series of numbers that are to be added or subtracted (or otherwise compared), it can be convenient to use the same value of <i>m</i> for all elements of the series. </p><p>Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized or differently normalized form, such as <a href="/wiki/Engineering_notation" title="Engineering notation">engineering notation</a>, is desired. Normalized scientific notation is often called <b><a href="/wiki/Exponentiation" title="Exponentiation">exponential</a> notation</b> – although the latter term is more general and also applies when <i>m</i> is not restricted to the range 1 to 10 (as in engineering notation for instance) and to <a href="/wiki/Base_(exponentiation)" title="Base (exponentiation)">bases</a> other than 10 (for example, <span style="white-space:nowrap">3.15<span style="margin-left:0.27em;margin-right:0.27em">×</span>2<span style="display:none">^</span><sup>20</sup></span>). </p> <div class="mw-heading mw-heading2"><h2 id="Engineering_notation">Engineering notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=3" title="Edit section: Engineering notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Engineering_notation" title="Engineering notation">Engineering notation</a></div> <p>Engineering notation (often named "ENG" on scientific calculators) differs from normalized scientific notation in that the exponent <i>n</i> is restricted to <a href="/wiki/Multiple_(mathematics)" title="Multiple (mathematics)">multiples</a> of 3. Consequently, the absolute value of <i>m</i> is in the range 1 ≤ |<i>m</i>| < 1000, rather than 1 ≤ |<i>m</i>| < 10. Though similar in concept, engineering notation is rarely called scientific notation. Engineering notation allows the numbers to explicitly match their corresponding <a href="/wiki/SI_prefixes" class="mw-redirect" title="SI prefixes">SI prefixes</a>, which facilitates reading and oral communication. For example, <span class="nowrap"><span data-sort-value="6992125000000000000♠"></span>12.5<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−9</sup> m</span> can be read as "twelve-point-five nanometres" and written as <span class="nowrap"><span data-sort-value="6992125000000000000♠"></span>12.5 nm</span>, while its scientific notation equivalent <span class="nowrap"><span data-sort-value="6992125000000000000♠"></span>1.25<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−8</sup> m</span> would likely be read out as "one-point-two-five times ten-to-the-negative-eight metres". </p> <div class="mw-heading mw-heading2"><h2 id="Significant_figures">Significant figures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=4" title="Edit section: Significant figures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Significant_figures" title="Significant figures">Significant figures</a></div> <p>A significant figure is a digit in a number that adds to its precision. This includes all nonzero numbers, zeroes between significant digits, and zeroes <a href="/wiki/Significant_figures#Identifying_significant_digits" title="Significant figures">indicated to be significant</a>. Leading and trailing zeroes are not significant digits, because they exist only to show the scale of the number. Unfortunately, this leads to ambiguity. The number <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1<span style="margin-left:.25em;">230</span><span style="margin-left:.25em;">400</span></span> is usually read to have five significant figures: 1, 2, 3, 0, and 4, the final two zeroes serving only as placeholders and adding no precision. The same number, however, would be used if the last two digits were also measured precisely and found to equal 0 – seven significant figures. </p><p>When a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the placeholding zeroes are no longer required. Thus <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1<span style="margin-left:.25em;">230</span><span style="margin-left:.25em;">400</span></span> would become <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1.2304<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>6</sup></span> if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1.230<span style="margin-left:.25em;">40</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>6</sup></span> or <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1.230<span style="margin-left:.25em;">400</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>6</sup></span>. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous. </p> <div class="mw-heading mw-heading3"><h3 id="Estimated_final_digits">Estimated final digits</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=5" title="Edit section: Estimated final digits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is customary in scientific measurement to record all the definitely known digits from the measurement and to estimate at least one additional digit if there is any information at all available on its value. The resulting number contains more information than it would without the extra digit, which may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together). </p><p>Additional information about precision can be conveyed through additional notation. It is often useful to know how exact the final digit or digits are. For instance, the accepted value of the mass of the <a href="/wiki/Proton" title="Proton">proton</a> can properly be expressed as <span class="nowrap"><span data-sort-value="6973167262192369000♠"></span>1.672<span style="margin-left:.25em;">621</span><span style="margin-left:.25em;">923</span><span style="margin-left:.25em;">69</span>(51)<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−27</sup> kg</span>, which is shorthand for <span class="nowrap"><span data-sort-value="6973167262192369000♠"></span>(1.672<span style="margin-left:.25em;">621</span><span style="margin-left:.25em;">923</span><span style="margin-left:.25em;">69</span><span style="margin-left:0.3em;margin-right:0.15em;">±</span>0.000<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">51</span>)<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−27</sup> kg</span>. However it is still unclear whether the error (<span class="nowrap"><span data-sort-value="6963510000000000000♠"></span>5.1<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−37</sup></span> in this case) is the maximum possible error, <a href="/wiki/Standard_error" title="Standard error">standard error</a>, or some other <a href="/wiki/Confidence_interval" title="Confidence interval">confidence interval</a>. </p> <div class="mw-heading mw-heading2"><h2 id="E_notation">E notation <span class="anchor" id="Q_notation"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=6" title="Edit section: E notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="float:right; margin: 0.5em 0 1.3em 1.4em"> <tbody><tr> <th>Explicit notation </th> <th>E notation </th></tr> <tr> <td><span class="nowrap"><span data-sort-value="7000200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>0</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">2E0</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7002300000000000000♠"></span>3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">3E2</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7003432176800000000♠"></span>4.321<span style="margin-left:.25em;">768</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>3</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">4.321768E3</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="2995470000000000000♠"></span>−5.3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>4</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">-5.3E4</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7009672000000000000♠"></span>6.72<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>9</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">6.72E9</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="6999200000000000000♠"></span>2<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−1</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">2E-1</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="7002986999999999999♠"></span>9.87<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">9.87E2</code> </td></tr> <tr> <td><span class="nowrap"><span data-sort-value="6991751000000000000♠"></span>7.51<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−9</sup></span> </td> <td><code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="background:none; border:none; color:inherit; padding: 0px 0px;" dir="ltr">7.51E-9</code> </td></tr></tbody></table> <p><a href="/wiki/Calculator" title="Calculator">Calculators</a> and <a href="/wiki/Computer_program" title="Computer program">computer programs</a> typically present very large or small numbers using scientific notation, and some can be configured to uniformly present all numbers that way. Because <a href="/wiki/Superscript" class="mw-redirect" title="Superscript">superscript</a> exponents like 10<sup>7</sup> can be inconvenient to display or type, the letter "E" or "e" (for "exponent") is often used to represent "times ten raised to the power of", so that the notation <span class="nowrap"><i>m</i> E <i>n</i></span> for a decimal significand <i>m</i> and integer exponent <i>n</i> means the same as <span class="nowrap"><i>m</i> × 10<sup><i>n</i></sup></span>. For example <a href="/wiki/Avogadro_constant" title="Avogadro constant"><span class="nowrap"><span data-sort-value="7023602200000000000♠"></span>6.022<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>23</sup></span></a> is written as <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">6.022E23</code> or <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">6.022e23</code>, and <a href="/wiki/Planck_length" class="mw-redirect" title="Planck length"><span class="nowrap"><span data-sort-value="6965160000000000000♠"></span>1.6<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−35</sup></span></a> is written as <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">1.6E-35</code> or <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">1.6e-35</code>. While common in computer output, this abbreviated version of scientific notation is discouraged for published documents by some style guides.<sup id="cite_ref-Edwards_2009_2-0" class="reference"><a href="#cite_note-Edwards_2009-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Most popular programming languages – including <a href="/wiki/Fortran" title="Fortran">Fortran</a>, <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a>/<a href="/wiki/C%2B%2B" title="C++">C++</a>, <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>, and <a href="/wiki/JavaScript" title="JavaScript">JavaScript</a> – use this "E" notation, which comes from Fortran and was present in the first version released for the <a href="/wiki/IBM_704" title="IBM 704">IBM 704</a> in 1956.<sup id="cite_ref-Fortran_4-0" class="reference"><a href="#cite_note-Fortran-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The E notation was already used by the developers of <a href="/wiki/SHARE_Operating_System" title="SHARE Operating System">SHARE Operating System</a> (SOS) for the <a href="/wiki/IBM_709" title="IBM 709">IBM 709</a> in 1958.<sup id="cite_ref-DiGri-King_1958_5-0" class="reference"><a href="#cite_note-DiGri-King_1958-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Later versions of Fortran (at least since <a href="/wiki/FORTRAN_IV" class="mw-redirect" title="FORTRAN IV">FORTRAN IV</a> as of 1961) also use "D" to signify <a href="/wiki/Double_precision" class="mw-redirect" title="Double precision">double precision</a> numbers in scientific notation,<sup id="cite_ref-UH-Manoa_6-0" class="reference"><a href="#cite_note-UH-Manoa-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and newer Fortran compilers use "Q" to signify <a href="/wiki/Quadruple_precision" class="mw-redirect" title="Quadruple precision">quadruple precision</a>.<sup id="cite_ref-FortranQ_7-0" class="reference"><a href="#cite_note-FortranQ-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/MATLAB" title="MATLAB">MATLAB</a> programming language supports the use of either "E" or "D". </p><p>The <a href="/wiki/ALGOL" title="ALGOL">ALGOL 60</a> (1960) programming language uses a subscript ten "<sub>10</sub>" character instead of the letter "E", for example: <code class="nowrap">6.022<sub>10</sub>23</code>.<sup id="cite_ref-Naur_1960_8-0" class="reference"><a href="#cite_note-Naur_1960-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Savard_2005_9-0" class="reference"><a href="#cite_note-Savard_2005-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> This presented a challenge for computer systems which did not provide such a character, so <a href="/wiki/ALGOL_W" title="ALGOL W">ALGOL W</a> (1966) replaced the symbol by a single quote, e.g. <code>6.022'+23</code>,<sup id="cite_ref-Bauer-Becker-Graham_1968_10-0" class="reference"><a href="#cite_note-Bauer-Becker-Graham_1968-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and some Soviet Algol variants allowed the use of the Cyrillic letter "<a href="/wiki/Yu_(Cyrillic)" title="Yu (Cyrillic)">ю</a>", e.g. <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">6.022ю+23</code>. Subsequently, the <a href="/wiki/ALGOL_68" title="ALGOL 68">ALGOL 68</a> programming language provided a choice of characters: <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">E</code>, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">e</code>, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">\</code>, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">⊥</code>, or <code><sub>10</sub></code>.<sup id="cite_ref-Algol_1973_11-0" class="reference"><a href="#cite_note-Algol_1973-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The ALGOL "<sub>10</sub>" character was included in the Soviet <a href="/wiki/GOST_10859" title="GOST 10859">GOST 10859</a> text encoding (1964), and was added to <a href="/wiki/Unicode" title="Unicode">Unicode</a> 5.2 (2009) as <span class="nowrap"><style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">U+23E8</span> </span><span style="font-size:125%;line-height:1em">⏨</span> <span style="font-variant: small-caps; text-transform: lowercase;">DECIMAL EXPONENT SYMBOL</span>.<sup id="cite_ref-Unicode_12-0" class="reference"><a href="#cite_note-Unicode-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Some programming languages use other symbols. For instance, <a href="/wiki/Simula" title="Simula">Simula</a> uses <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">&</code> (or <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">&&</code> for <a href="/wiki/Double_precision" class="mw-redirect" title="Double precision">long</a>), as in <code class="nowrap mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">6.022&23</code>.<sup id="cite_ref-SIMULA_1986_13-0" class="reference"><a href="#cite_note-SIMULA_1986-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a> supports the shorthand notation <code class="nowrap mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">6.022*^23</code> (reserving the letter <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">E</code> for the <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">mathematical constant <i>e</i></a>). </p><p><span class="anchor" id="Decapower"></span><span class="anchor" id="D_notation"></span> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Avogadro%27s_number_in_e_notation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Avogadro%27s_number_in_e_notation.jpg/220px-Avogadro%27s_number_in_e_notation.jpg" decoding="async" width="220" height="47" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Avogadro%27s_number_in_e_notation.jpg/330px-Avogadro%27s_number_in_e_notation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Avogadro%27s_number_in_e_notation.jpg/440px-Avogadro%27s_number_in_e_notation.jpg 2x" data-file-width="2955" data-file-height="631" /></a><figcaption>A <a href="/wiki/Texas_Instruments" title="Texas Instruments">Texas Instruments</a> <a href="/wiki/TI-84_Plus_series" title="TI-84 Plus series">TI-84 Plus</a> calculator display showing the <a href="/wiki/Avogadro_constant" title="Avogadro constant">Avogadro constant</a> to three significant figures in E notation</figcaption></figure> <p>The first <a href="/wiki/Pocket_calculator" class="mw-redirect" title="Pocket calculator">pocket calculators</a> supporting scientific notation appeared in 1972.<sup id="cite_ref-TI_1973_SR-10_14-0" class="reference"><a href="#cite_note-TI_1973_SR-10-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> To enter numbers in scientific notation calculators include a button labeled "EXP" or "×10<sup><i>x</i></sup>", among other variants. The displays of pocket calculators of the 1970s did not display an explicit symbol between significand and exponent; instead, one or more digits were left blank (e.g. <code>6.022 23</code>, as seen in the <a href="/wiki/HP-25" title="HP-25">HP-25</a>), or a pair of smaller and slightly raised digits were reserved for the exponent (e.g. <code>6.022 <sup>23</sup></code>, as seen in the <a href="/wiki/Commodore_International" title="Commodore International">Commodore PR100</a>). In 1976, <a href="/wiki/Hewlett-Packard" title="Hewlett-Packard">Hewlett-Packard</a> calculator user Jim Davidson coined the term <i>decapower</i> for the scientific-notation exponent to distinguish it from "normal" exponents, and suggested the letter "D" as a separator between significand and exponent in typewritten numbers (for example, <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">6.022D23</code>); these gained some currency in the programmable calculator user community.<sup id="cite_ref-Decapower_15-0" class="reference"><a href="#cite_note-Decapower-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The letters "E" or "D" were used as a scientific-notation separator by <a href="/wiki/Sharp_Corporation" title="Sharp Corporation">Sharp</a> <a href="/wiki/Pocket_computer" title="Pocket computer">pocket computers</a> released between 1987 and 1995, "E" used for 10-digit numbers and "D" used for 20-digit double-precision numbers.<sup id="cite_ref-Sharp_16-0" class="reference"><a href="#cite_note-Sharp-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Texas_Instruments" title="Texas Instruments">Texas Instruments</a> <a href="/wiki/TI-83_series" title="TI-83 series">TI-83</a> and <a href="/wiki/TI-84_Plus_series" title="TI-84 Plus series">TI-84</a> series of calculators (1996–present) use a <a href="/wiki/Small_caps" title="Small caps">small capital</a> <code><small>E</small></code> for the separator.<sup id="cite_ref-TI-83_17-0" class="reference"><a href="#cite_note-TI-83-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>In 1962, Ronald O. Whitaker of Rowco Engineering Co. proposed a power-of-ten system nomenclature where the exponent would be circled, e.g. 6.022 × 10<sup>3</sup> would be written as "6.022③".<sup id="cite_ref-Whitaker_1962_18-0" class="reference"><a href="#cite_note-Whitaker_1962-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Use_of_spaces">Use of spaces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=7" title="Edit section: Use of spaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In normalized scientific notation, in E notation, and in engineering notation, the <a href="/wiki/Space_(punctuation)" title="Space (punctuation)">space</a> (which in <a href="/wiki/Typesetting" title="Typesetting">typesetting</a> may be represented by a normal width space or a <a href="/wiki/Thin_space" title="Thin space">thin space</a>) that is allowed <i>only</i> before and after "×" or in front of "E" is sometimes omitted, though it is less common to do so before the alphabetical character.<sup id="cite_ref-Samples_19-0" class="reference"><a href="#cite_note-Samples-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Further_examples_of_scientific_notation">Further examples of scientific notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=8" title="Edit section: Further examples of scientific notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>An <a href="/wiki/Electron" title="Electron">electron</a>'s mass is about <span class="nowrap"><span data-sort-value="6969910938355999999♠"></span>0.000<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">910</span><span style="margin-left:.25em;">938</span><span style="margin-left:.25em;">356</span> kg</span>.<sup id="cite_ref-CODATA2014Full_20-0" class="reference"><a href="#cite_note-CODATA2014Full-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In scientific notation, this is written <span class="nowrap"><span data-sort-value="6969910938355999999♠"></span>9.109<span style="margin-left:.25em;">383</span><span style="margin-left:.25em;">56</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−31</sup> kg</span>.</li> <li>The <a href="/wiki/Earth" title="Earth">Earth</a>'s <a href="/wiki/Mass" title="Mass">mass</a> is about <span class="nowrap"><span data-sort-value="7024597240000000000♠"></span>5<span style="margin-left:.25em;">972</span><span style="margin-left:.25em;">400</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span> kg</span>.<sup id="cite_ref-Luzum_2011_21-0" class="reference"><a href="#cite_note-Luzum_2011-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> In scientific notation, this is written <span class="nowrap"><span data-sort-value="7024597240000000000♠"></span>5.9724<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>24</sup> kg</span>.</li> <li>The <a href="/wiki/Earth#Size_and_shape" title="Earth">Earth's circumference</a> is approximately <span class="nowrap"><span data-sort-value="7007400000000000000♠"></span>40<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span> m</span>.<sup id="cite_ref-Lide_2000_22-0" class="reference"><a href="#cite_note-Lide_2000-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> In scientific notation, this is <span class="nowrap"><span data-sort-value="7007400000000000000♠"></span>4<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>7</sup> m</span>. In engineering notation, this is written <span class="nowrap"><span data-sort-value="7007400000000000000♠"></span>40<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>6</sup> m</span>. In <a href="/wiki/International_System_of_Units" title="International System of Units">SI writing style</a>, this may be written <span class="nowrap"><span data-sort-value="7007400000000000000♠"></span>40 Mm</span> (<i><span class="nowrap"><span data-sort-value="7001400000000000000♠"></span>40 megametres</span></i>).</li> <li>An <a href="/wiki/Inch" title="Inch">inch</a> is defined as <i>exactly</i> <span class="nowrap"><span data-sort-value="6998254000000000000♠"></span>25.4 mm</span>. Using scientific notation, this value can be uniformly expressed to any desired precision, from the nearest tenth of a <a href="/wiki/Millimeter" class="mw-redirect" title="Millimeter">millimeter</a> <span class="nowrap"><span data-sort-value="6998254000000000000♠"></span>2.54<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>1</sup> mm</span> to the nearest <a href="/wiki/Nanometer" class="mw-redirect" title="Nanometer">nanometer</a> <span class="nowrap"><span data-sort-value="6998254000000000000♠"></span>2.540<span style="margin-left:.25em;">0000</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>1</sup> mm</span>, or beyond.</li> <li><a href="/wiki/Hyperinflation" title="Hyperinflation">Hyperinflation</a> means that too much money is put into circulation, perhaps by printing banknotes, chasing too few goods. It is sometimes defined as inflation of 50% or more in a single month. In such conditions, money rapidly loses its value. Some countries have had events of inflation of 1 million percent or more in a single month, which usually results in the rapid abandonment of the currency. For example, in November 2008 the monthly inflation rate of the <a href="/wiki/Zimbabwean_dollar" title="Zimbabwean dollar">Zimbabwean dollar</a> reached 79.6 billion percent (470% per day); the approximate value with three significant figures would be <span class="nowrap"><span data-sort-value="7010796000000000000♠"></span>7.96<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>10</sup></span> %,<sup id="cite_ref-Kadzere_2008_23-0" class="reference"><a href="#cite_note-Kadzere_2008-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-BBC_24-0" class="reference"><a href="#cite_note-BBC-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> or more simply a rate of <span class="nowrap"><span data-sort-value="7008796000000000000♠"></span>7.96<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>8</sup></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Converting_numbers">Converting numbers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=9" title="Edit section: Converting numbers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation. None of these alter the actual number, only how it's expressed. </p> <div class="mw-heading mw-heading3"><h3 id="Decimal_to_scientific">Decimal to scientific</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=10" title="Edit section: Decimal to scientific"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>First, move the decimal separator point sufficient places, <i>n</i>, to put the number's value within a desired range, between 1 and 10 for normalized notation. If the decimal was moved to the left, append <code class="nowrap">× 10<i><sup>n</sup></i></code>; to the right, <code class="nowrap">× 10<i><sup>−n</sup></i></code>. To represent the number <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1,230,400</span> in normalized scientific notation, the decimal separator would be moved 6 digits to the left and <code class="nowrap">× 10<sup>6</sup></code> appended, resulting in <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1.2304<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>6</sup></span>. The number <span class="nowrap"><span data-sort-value="3002596790000000000♠"></span>−0.004<span style="margin-left:.25em;">0321</span></span> would have its decimal separator shifted 3 digits to the right instead of the left and yield <span class="nowrap"><span data-sort-value="3002596790000000000♠"></span>−4.0321<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup></span> as a result. </p> <div class="mw-heading mw-heading3"><h3 id="Scientific_to_decimal">Scientific to decimal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=11" title="Edit section: Scientific to decimal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Converting a number from scientific notation to decimal notation, first remove the <code class="nowrap">× 10<i><sup>n</sup></i></code> on the end, then shift the decimal separator <i>n</i> digits to the right (positive <i>n</i>) or left (negative <i>n</i>). The number <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1.2304<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>6</sup></span> would have its decimal separator shifted 6 digits to the right and become <span class="nowrap"><span data-sort-value="7006123040000000000♠"></span>1,230,400</span>, while <span class="nowrap"><span data-sort-value="3002596790000000000♠"></span>−4.0321<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup></span> would have its decimal separator moved 3 digits to the left and be <span class="nowrap"><span data-sort-value="3002596790000000000♠"></span>−0.004<span style="margin-left:.25em;">0321</span></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Exponential">Exponential</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=12" title="Edit section: Exponential"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The decimal separator in the significand is shifted <i>x</i> places to the left (or right) and <i>x</i> is added to (or subtracted from) the exponent, as shown below. </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.5em;"><span class="nowrap"><span data-sort-value="7003123400000000000♠"></span>1.234<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>3</sup></span> = <span class="nowrap"><span data-sort-value="7003123400000000000♠"></span>12.34<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>2</sup></span> = <span class="nowrap"><span data-sort-value="7003123400000000000♠"></span>123.4<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>1</sup></span> = 1234</div> <div class="mw-heading mw-heading2"><h2 id="Basic_operations">Basic operations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=13" title="Edit section: Basic operations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Given two numbers in scientific notation, <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be15afaf9428841c117877358dbb062ffcb5db25" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.792ex; height:2.676ex;" alt="{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07e27f72849ba37609641e63f6a630f03ecfcc7a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.792ex; height:2.676ex;" alt="{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}"></span> </p><p><a href="/wiki/Multiplication" title="Multiplication">Multiplication</a> and <a href="/wiki/Division_(mathematics)" title="Division (mathematics)">division</a> are performed using the rules for operation with <a href="/wiki/Exponentiation" title="Exponentiation">exponentiation</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f001c20e0deb1a0775c081a23593cb3256f1c5fc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.367ex; height:2.843ex;" alt="{\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b538be3f091619f0cf3ad207f7b5ec41d266172" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.561ex; height:5.009ex;" alt="{\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}}"></span> </p><p>Some examples are: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5.67\times 10^{-5}\times 2.34\times 10^{2}\approx 13.3\times 10^{-5+2}=13.3\times 10^{-3}=1.33\times 10^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5.67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>×</mo> <mn>2.34</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>≈</mo> <mn>13.3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> <mo>+</mo> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>13.3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>1.33</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5.67\times 10^{-5}\times 2.34\times 10^{2}\approx 13.3\times 10^{-5+2}=13.3\times 10^{-3}=1.33\times 10^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b20d04f35711114c0c57ede6efaa89fdc586af8d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:71.119ex; height:2.676ex;" alt="{\displaystyle 5.67\times 10^{-5}\times 2.34\times 10^{2}\approx 13.3\times 10^{-5+2}=13.3\times 10^{-3}=1.33\times 10^{-2}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {2.34\times 10^{2}}{5.67\times 10^{-5}}}\approx 0.413\times 10^{2-(-5)}=0.413\times 10^{7}=4.13\times 10^{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2.34</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>5.67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>≈</mo> <mn>0.413</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>−</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <mn>0.413</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mo>=</mo> <mn>4.13</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2.34\times 10^{2}}{5.67\times 10^{-5}}}\approx 0.413\times 10^{2-(-5)}=0.413\times 10^{7}=4.13\times 10^{6}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4868a4340cc49bc3dbb04fc261cc5c23fd1499f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:59.808ex; height:6.176ex;" alt="{\displaystyle {\frac {2.34\times 10^{2}}{5.67\times 10^{-5}}}\approx 0.413\times 10^{2-(-5)}=0.413\times 10^{7}=4.13\times 10^{6}}"></span> </p><p><a href="/wiki/Addition" title="Addition">Addition</a> and <a href="/wiki/Subtraction" title="Subtraction">subtraction</a> require the numbers to be represented using the same exponential part, so that the significand can be simply added or subtracted: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.5em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be15afaf9428841c117877358dbb062ffcb5db25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.792ex; height:2.676ex;" alt="{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07e27f72849ba37609641e63f6a630f03ecfcc7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.792ex; height:2.676ex;" alt="{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}}"></span> with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{0}=n_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{0}=n_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b129fbad013eb8d73305ff2edddead78d197f766" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.996ex; height:2.009ex;" alt="{\displaystyle n_{0}=n_{1}}"></span></div> <p>Next, add or subtract the significands: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>±</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>±</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76e54be749bf3de6883c697b97c3652e22017455" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.761ex; height:2.843ex;" alt="{\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}}"></span> </p><p>An example: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2.34</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>+</mo> <mn>5.67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mo>=</mo> <mn>2.34</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>+</mo> <mn>0.567</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>=</mo> <mn>2.907</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5023254d2a7df1e9cff7a47d8bbea37de3167602" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:72.364ex; height:2.843ex;" alt="{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Other_bases">Other bases <span class="anchor" id="B_notation"></span><span class="anchor" id="H_notation"></span><span class="anchor" id="O_notation"></span><span class="anchor" id="C_notation"></span><span class="anchor" id="P_notation"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=14" title="Edit section: Other bases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While base ten is normally used for scientific notation, powers of other bases can be used too,<sup id="cite_ref-TI_1974_SR-22_25-0" class="reference"><a href="#cite_note-TI_1974_SR-22-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> base 2 being the next most commonly used one. </p><p>For example, in base-2 scientific notation, the number 1001<sub>b</sub> in <a href="/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a> (=9<sub>d</sub>) is written as <span class="nowrap">1.001<sub>b</sub> × 2<sub>d</sub><sup>11<sub>b</sub></sup></span> or <span class="nowrap">1.001<sub>b</sub> × 10<sub>b</sub><sup>11<sub>b</sub></sup></span> using binary numbers (or shorter <span class="nowrap">1.001 × 10<sup>11</sup></span> if binary context is obvious).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2024)">citation needed</span></a></i>]</sup> In E notation, this is written as <span class="nowrap">1.001<sub>b</sub>E11<sub>b</sub></span> (or shorter: 1.001E11) with the letter "E" now standing for "times two (10<sub>b</sub>) to the power" here. In order to better distinguish this base-2 exponent from a base-10 exponent, a base-2 exponent is sometimes also indicated by using the letter "B" instead of "E",<sup id="cite_ref-HP16C-Lib_26-0" class="reference"><a href="#cite_note-HP16C-Lib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> a shorthand notation originally proposed by <a href="/w/index.php?title=Bruce_Alan_Martin&action=edit&redlink=1" class="new" title="Bruce Alan Martin (page does not exist)">Bruce Alan Martin</a> of <a href="/wiki/Brookhaven_National_Laboratory" title="Brookhaven National Laboratory">Brookhaven National Laboratory</a> in 1968,<sup id="cite_ref-Martin_1968_27-0" class="reference"><a href="#cite_note-Martin_1968-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> as in <span class="nowrap">1.001<sub>b</sub>B11<sub>b</sub></span> (or shorter: 1.001B11). For comparison, the same number in <a href="/wiki/Decimal_representation" title="Decimal representation">decimal representation</a>: <span class="nowrap">1.125 × 2<sup>3</sup></span> (using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes <span class="nowrap">1.001<sub>b</sub> × 10<sub>b</sub><sup>3<sub>d</sub></sup></span> or shorter 1.001B3.<sup id="cite_ref-HP16C-Lib_26-1" class="reference"><a href="#cite_note-HP16C-Lib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>This is closely related to the base-2 <a href="/wiki/Floating-point" class="mw-redirect" title="Floating-point">floating-point</a> representation commonly used in computer arithmetic, and the usage of IEC <a href="/wiki/Binary_prefixes" class="mw-redirect" title="Binary prefixes">binary prefixes</a> (e.g. 1B10 for 1×2<sup>10</sup> (<a href="/wiki/Kibi-" class="mw-redirect" title="Kibi-">kibi</a>), 1B20 for 1×2<sup>20</sup> (<a href="/wiki/Mebi-" class="mw-redirect" title="Mebi-">mebi</a>), 1B30 for 1×2<sup>30</sup> (<a href="/wiki/Gibi-" class="mw-redirect" title="Gibi-">gibi</a>), 1B40 for 1×2<sup>40</sup> (<a href="/wiki/Tebi-" class="mw-redirect" title="Tebi-">tebi</a>)). </p><p>Similar to "B" (or "b"<sup id="cite_ref-HP16C-Add_28-0" class="reference"><a href="#cite_note-HP16C-Add-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup>), the letters "H"<sup id="cite_ref-HP16C-Lib_26-2" class="reference"><a href="#cite_note-HP16C-Lib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> (or "h"<sup id="cite_ref-HP16C-Add_28-1" class="reference"><a href="#cite_note-HP16C-Add-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup>) and "O"<sup id="cite_ref-HP16C-Lib_26-3" class="reference"><a href="#cite_note-HP16C-Lib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> (or "o",<sup id="cite_ref-HP16C-Add_28-2" class="reference"><a href="#cite_note-HP16C-Add-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> or "C"<sup id="cite_ref-HP16C-Lib_26-4" class="reference"><a href="#cite_note-HP16C-Lib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>) are sometimes also used to indicate <i>times 16 or 8 to the power</i> as in 1.25 = <span class="nowrap">1.40<sub>h</sub> × 10<sub>h</sub><sup>0<sub>h</sub></sup></span> = 1.40H0 = 1.40h0, or 98000 = <span class="nowrap">2.7732<sub>o</sub> × 10<sub>o</sub><sup>5<sub>o</sub></sup></span> = 2.7732o5 = 2.7732C5.<sup id="cite_ref-HP16C-Lib_26-5" class="reference"><a href="#cite_note-HP16C-Lib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>Another similar convention to denote base-2 exponents is using a letter "P" (or "p", for "power"). In this notation the significand is always meant to be hexadecimal, whereas the exponent is always meant to be decimal.<sup id="cite_ref-Rationale_2003_C_29-0" class="reference"><a href="#cite_note-Rationale_2003_C-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> This notation can be produced by implementations of the <i><a href="/wiki/Printf" title="Printf">printf</a></i> family of functions following the <a href="/wiki/C99" title="C99">C99</a> specification and (<a href="/wiki/Single_Unix_Specification" class="mw-redirect" title="Single Unix Specification">Single Unix Specification</a>) <a href="/wiki/IEEE_Std_1003.1" class="mw-redirect" title="IEEE Std 1003.1">IEEE Std 1003.1</a> <a href="/wiki/POSIX" title="POSIX">POSIX</a> standard, when using the <i>%a</i> or <i>%A</i> conversion specifiers.<sup id="cite_ref-Rationale_2003_C_29-1" class="reference"><a href="#cite_note-Rationale_2003_C-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-printf_2013_30-0" class="reference"><a href="#cite_note-printf_2013-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Beebe_2017_Hex_31-0" class="reference"><a href="#cite_note-Beebe_2017_Hex-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Starting with <a href="/wiki/C%2B%2B11" title="C++11">C++11</a>, <a href="/wiki/C%2B%2B" title="C++">C++</a> I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard since <a href="/wiki/C%2B%2B17" title="C++17">C++17</a>.<sup id="cite_ref-C++17_32-0" class="reference"><a href="#cite_note-C++17-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Apple_Inc." title="Apple Inc.">Apple</a>'s <a href="/wiki/Swift_(programming_language)" title="Swift (programming language)">Swift</a> supports it as well.<sup id="cite_ref-Swift_2017_33-0" class="reference"><a href="#cite_note-Swift_2017-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> It is also required by the <a href="/wiki/IEEE_754-2008" class="mw-redirect" title="IEEE 754-2008">IEEE 754-2008</a> binary floating-point standard. Example: 1.3DEp42 represents <span class="nowrap">1.3DE<sub>h</sub> × 2<sup>42</sup></span>. </p><p><a href="/wiki/Engineering_notation" title="Engineering notation">Engineering notation</a> can be viewed as a base-1000 scientific notation. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Positional_notation" title="Positional notation">Positional notation</a></li> <li><a href="/wiki/ISO/IEC_80000" title="ISO/IEC 80000">ISO/IEC 80000</a> – an international standard which guides the use of physical quantities and units of measurement in science</li> <li><a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou numerals</a> – a Chinese numeral system formerly used in commerce, with order of magnitude written below the significand</li> <li><a href="/wiki/RKM_code" title="RKM code">RKM code</a> – a notation to specify resistor and capacitor values, with symbols for powers of 1000</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Scientific_notation&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Calio_2017-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Calio_2017_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCaliòAlessandro2017" class="citation book cs1">Caliò, Franca; Alessandro, Lazzari (September 2017). <i>Elements of Mathematics with Numerical Applications</i>. Società Editrice Esculapio. pp. 30–32. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-8-89385052-0" title="Special:BookSources/978-8-89385052-0"><bdi>978-8-89385052-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elements+of+Mathematics+with+Numerical+Applications&rft.pages=30-32&rft.pub=Societ%C3%A0+Editrice+Esculapio&rft.date=2017-09&rft.isbn=978-8-89385052-0&rft.aulast=Cali%C3%B2&rft.aufirst=Franca&rft.au=Alessandro%2C+Lazzari&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Edwards_2009-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Edwards_2009_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdwards2009" class="citation book cs1">Edwards, John (2009). <a rel="nofollow" class="external text" href="http://hps.org/documents/2010_midyear_author-submission-guidelines.pdf"><i>Submission Guidelines for Authors: HPS 2010 Midyear Proceedings</i></a> <span class="cs1-format">(PDF)</span>. McLean, VA: Health Physics Society. p. 5<span class="reference-accessdate">. Retrieved <span class="nowrap">2013-03-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Submission+Guidelines+for+Authors%3A+HPS+2010+Midyear+Proceedings&rft.place=McLean%2C+VA&rft.pages=5&rft.pub=Health+Physics+Society&rft.date=2009&rft.aulast=Edwards&rft.aufirst=John&rft_id=http%3A%2F%2Fhps.org%2Fdocuments%2F2010_midyear_author-submission-guidelines.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCoghillGarsonAmerican_Chemical_Society2006" class="citation book cs1">Coghill, Anne M.; Garson, Lorrin R.; American Chemical Society, eds. (2006). <a rel="nofollow" class="external text" href="https://www.worldcat.org/title/ocm62872860"><i>The ACS style guide: effective communication of scientific information</i></a> (3rd ed.). Washington, DC : Oxford; New York: American Chemical Society; Oxford University Press. p. 210. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8412-3999-9" title="Special:BookSources/978-0-8412-3999-9"><bdi>978-0-8412-3999-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/62872860">62872860</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+ACS+style+guide%3A+effective+communication+of+scientific+information&rft.place=Washington%2C+DC+%3A+Oxford%3B+New+York&rft.pages=210&rft.edition=3rd&rft.pub=American+Chemical+Society%3B+Oxford+University+Press&rft.date=2006&rft_id=info%3Aoclcnum%2Focm62872860&rft.isbn=978-0-8412-3999-9&rft_id=https%3A%2F%2Fwww.worldcat.org%2Ftitle%2Focm62872860&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Fortran-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fortran_4-0">^</a></b></span> <span class="reference-text">However, E notation was not included in the preliminary specification of Fortran, as of 1954. <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBackusHerrickNelsonZiller1954" class="citation book cs1"><a href="/wiki/John_Warner_Backus" class="mw-redirect" title="John Warner Backus">Backus, John Warner</a>, ed. (1954-11-10). <a rel="nofollow" class="external text" href="https://archive.computerhistory.org/resources/text/Fortran/102679231.05.01.acc.pdf"><i>Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN</i></a> <span class="cs1-format">(PDF)</span> (Preliminary report). New York: Programming Research Group, Applied Science Division, <a href="/wiki/International_Business_Machines_Corporation" class="mw-redirect" title="International Business Machines Corporation">International Business Machines Corporation</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-07-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Specifications+for%3A+The+IBM+Mathematical+FORmula+TRANSlating+System%2C+FORTRAN&rft.place=New+York&rft.pub=Programming+Research+Group%2C+Applied+Science+Division%2C+International+Business+Machines+Corporation&rft.date=1954-11-10&rft.aulast=Backus&rft.aufirst=John+Warner&rft.au=Herrick%2C+Harlan+L.&rft.au=Nelson%2C+Robert+A.&rft.au=Ziller%2C+Irving&rft_id=https%3A%2F%2Farchive.computerhistory.org%2Fresources%2Ftext%2FFortran%2F102679231.05.01.acc.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (29 pages) <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBackusBeeberBestGoldberg1956" class="citation book cs1"><a href="/wiki/David_Sayre" title="David Sayre">Sayre, David</a>, ed. (1956-10-15). <a rel="nofollow" class="external text" href="http://archive.computerhistory.org/resources/text/Fortran/102649787.05.01.acc.pdf"><i>The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual</i></a> <span class="cs1-format">(PDF)</span>. New York: Applied Science Division and Programming Research Department, <a href="/wiki/International_Business_Machines_Corporation" class="mw-redirect" title="International Business Machines Corporation">International Business Machines Corporation</a>. pp. 9, 27<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-07-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+FORTRAN+Automatic+Coding+System+for+the+IBM+704+EDPM%3A+Programmer%27s+Reference+Manual&rft.place=New+York&rft.pages=9%2C+27&rft.pub=Applied+Science+Division+and+Programming+Research+Department%2C+International+Business+Machines+Corporation&rft.date=1956-10-15&rft.aulast=Backus&rft.aufirst=John+Warner&rft.au=Beeber%2C+Robert+J.&rft.au=Best%2C+Sheldon+F.&rft.au=Goldberg%2C+Richard&rft.au=Herrick%2C+Harlan+L.&rft.au=Hughes%2C+Robert+A.&rft.au=Mitchell+%28Haibt%29%2C+Lois+B.&rft.au=Nelson%2C+Robert+A.&rft.au=Nutt%2C+Roy&rft.au=Sayre%2C+David&rft.au=Sheridan%2C+Peter+B.&rft.au=Stern%2C+Harold&rft.au=Ziller%2C+Irving&rft_id=http%3A%2F%2Farchive.computerhistory.org%2Fresources%2Ftext%2FFortran%2F102649787.05.01.acc.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (2+51+1 pages) </p> </span></li> <li id="cite_note-DiGri-King_1958-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-DiGri-King_1958_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDiGriKing1959" class="citation journal cs1">DiGri, Vincent J.; King, Jane E. (April 1959) [1958-06-11]. <a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F320964.320969">"The SHARE 709 System: Input-Output Translation"</a>. <i><a href="/wiki/Journal_of_the_ACM" title="Journal of the ACM">Journal of the ACM</a></i>. <b>6</b> (2): 141–144. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F320964.320969">10.1145/320964.320969</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:19660148">19660148</a>. <q>It tells the input translator that the field to be converted is a decimal number of the form ~X.XXXXE ± YY where E implies that the value of ~x.xxxx is to be scaled by ten to the ±YY power.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+ACM&rft.atitle=The+SHARE+709+System%3A+Input-Output+Translation&rft.volume=6&rft.issue=2&rft.pages=141-144&rft.date=1959-04&rft_id=info%3Adoi%2F10.1145%2F320964.320969&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A19660148%23id-name%3DS2CID&rft.aulast=DiGri&rft.aufirst=Vincent+J.&rft.au=King%2C+Jane+E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1145%252F320964.320969&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (4 pages) (NB. This was presented at the ACM meeting 11–13 June 1958.)</span> </li> <li id="cite_note-UH-Manoa-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-UH-Manoa_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.math.hawaii.edu/lab/197/fortran/fort3.htm#double">"UH Mānoa Mathematics » Fortran lesson 3: Format, Write, etc"</a>. Math.hawaii.edu. 2012-02-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-03-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=UH+M%C4%81noa+Mathematics+%C2%BB+Fortran+lesson+3%3A+Format%2C+Write%2C+etc.&rft.pub=Math.hawaii.edu&rft.date=2012-02-12&rft_id=http%3A%2F%2Fwww.math.hawaii.edu%2Flab%2F197%2Ffortran%2Ffort3.htm%23double&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-FortranQ-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FortranQ_7-0">^</a></b></span> <span class="reference-text"> For instance, DEC FORTRAN 77 (f77), <a href="/wiki/Intel_Fortran" class="mw-redirect" title="Intel Fortran">Intel Fortran</a>, Compaq/Digital Visual Fortran, and <a href="/wiki/GNU_Fortran" title="GNU Fortran">GNU Fortran</a> (gfortran) <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">"Double Precision, REAL**16". <a rel="nofollow" class="external text" href="https://wwwth.mpp.mpg.de/members/hahn/decfortman.html"><i>DEC Fortran 77 Manual</i></a>. <a href="/wiki/Digital_Equipment_Corporation" title="Digital Equipment Corporation">Digital Equipment Corporation</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-12-21</span></span>. <q>Digital Fortran 77 also allows the syntax Qsnnn, if the exponent field is within the T_floating double precision range. […] A REAL*16 constant is a basic real constant or an integer constant followed by a decimal exponent. A decimal exponent has the form: Qsnn […] s is an optional sign […] nn is a string of decimal digits […] This type of constant is only available on <a href="/wiki/DEC_Alpha" title="DEC Alpha">Alpha systems</a>.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Double+Precision%2C+REAL%2A%2A16&rft.btitle=DEC+Fortran+77+Manual&rft.pub=Digital+Equipment+Corporation&rft_id=https%3A%2F%2Fwwwth.mpp.mpg.de%2Fmembers%2Fhahn%2Fdecfortman.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://www.ehu.eus/sgi/ARCHIVOS/lang_for.pdf"><i>Intel Fortran: Language Reference</i></a> <span class="cs1-format">(PDF)</span>. <a href="/wiki/Intel_Corporation" class="mw-redirect" title="Intel Corporation">Intel Corporation</a>. 2005 [2003]. pp. 3-7–3-8, 3–10. 253261-003<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-12-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Intel+Fortran%3A+Language+Reference&rft.pages=3-7-3-8%2C+3-10&rft.pub=Intel+Corporation&rft.date=2005&rft_id=https%3A%2F%2Fwww.ehu.eus%2Fsgi%2FARCHIVOS%2Flang_for.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (858 pages) <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://jp.xlsoft.com/documents/intel/cvf/cvf_lref.pdf"><i>Compaq Visual Fortran – Language Reference</i></a> <span class="cs1-format">(PDF)</span>. Houston: <a href="/wiki/Compaq_Computer_Corporation" class="mw-redirect" title="Compaq Computer Corporation">Compaq Computer Corporation</a>. August 2001<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-12-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Compaq+Visual+Fortran+%E2%80%93+Language+Reference&rft.place=Houston&rft.pub=Compaq+Computer+Corporation&rft.date=2001-08&rft_id=https%3A%2F%2Fjp.xlsoft.com%2Fdocuments%2Fintel%2Fcvf%2Fcvf_lref.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (1441 pages) <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">"6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter". <a rel="nofollow" class="external text" href="https://gcc.gnu.org/onlinedocs/gcc-4.7.4/gfortran/_003ccode_003eQ_003c_002fcode_003e-exponent-letter.html#_003ccode_003eQ_003c_002fcode_003e-exponent-letter"><i>The GNU Fortran Compiler</i></a>. 2014-06-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=6.+Extensions%3A+6.1+Extensions+implemented+in+GNU+Fortran%3A+6.1.8+Q+exponent-letter&rft.btitle=The+GNU+Fortran+Compiler&rft.date=2014-06-12&rft_id=https%3A%2F%2Fgcc.gnu.org%2Fonlinedocs%2Fgcc-4.7.4%2Fgfortran%2F_003ccode_003eQ_003c_002fcode_003e-exponent-letter.html%23_003ccode_003eQ_003c_002fcode_003e-exponent-letter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> </p> </span></li> <li id="cite_note-Naur_1960-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Naur_1960_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNaur1960" class="citation book cs1"><a href="/wiki/Peter_Naur" title="Peter Naur">Naur, Peter</a>, ed. (1960). <a rel="nofollow" class="external text" href="https://dl.acm.org/doi/10.1145/367236.367262"><i>Report on the Algorithmic Language ALGOL 60</i></a>. Copenhagen.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Report+on+the+Algorithmic+Language+ALGOL+60&rft.place=Copenhagen&rft.date=1960&rft_id=https%3A%2F%2Fdl.acm.org%2Fdoi%2F10.1145%2F367236.367262&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-Savard_2005-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Savard_2005_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSavard2018" class="citation web cs1">Savard, John J. G. (2018) [2005]. <a rel="nofollow" class="external text" href="http://www.quadibloc.com/comp/cp02.htm">"Computer Arithmetic"</a>. <i>quadibloc</i>. The Early Days of Hexadecimal<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-07-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=quadibloc&rft.atitle=Computer+Arithmetic&rft.pages=The+Early+Days+of+Hexadecimal&rft.date=2018&rft.aulast=Savard&rft.aufirst=John+J.+G.&rft_id=http%3A%2F%2Fwww.quadibloc.com%2Fcomp%2Fcp02.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Bauer-Becker-Graham_1968-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bauer-Becker-Graham_1968_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBauerBeckerGraham1968" class="citation web cs1">Bauer, Henry R.; Becker, Sheldon; Graham, Susan L. (January 1968). <a rel="nofollow" class="external text" href="http://i.stanford.edu/pub/cstr/reports/cs/tr/68/86/CS-TR-68-86.pdf">"ALGOL W – Notes For Introductory Computer Science Courses"</a> <span class="cs1-format">(PDF)</span>. <a href="/wiki/Stanford_University" title="Stanford University">Stanford University</a>, Computer Science Department<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-04-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=ALGOL+W+%E2%80%93+Notes+For+Introductory+Computer+Science+Courses&rft.pub=Stanford+University%2C+Computer+Science+Department&rft.date=1968-01&rft.aulast=Bauer&rft.aufirst=Henry+R.&rft.au=Becker%2C+Sheldon&rft.au=Graham%2C+Susan+L.&rft_id=http%3A%2F%2Fi.stanford.edu%2Fpub%2Fcstr%2Freports%2Fcs%2Ftr%2F68%2F86%2FCS-TR-68-86.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Algol_1973-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Algol_1973_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">"Revised Report on the Algorithmic Language Algol 68". <i>Acta Informatica</i>. <b>5</b> (1–3): 1–236. September 1973. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.3999">10.1.1.219.3999</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00265077">10.1007/BF00265077</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:2490556">2490556</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Informatica&rft.atitle=Revised+Report+on+the+Algorithmic+Language+Algol+68&rft.volume=5&rft.issue=1%E2%80%933&rft.pages=1-236&rft.date=1973-09&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.219.3999%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A2490556%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF00265077&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Unicode-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Unicode_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBroukhis2008" class="citation cs2">Broukhis, Leonid (2008-01-22), <a rel="nofollow" class="external text" href="https://www.unicode.org/L2/L2008/08030r-subscript10.pdf">"Revised proposal to encode the decimal exponent symbol"</a> <span class="cs1-format">(PDF)</span>, <i>unicode.org</i> (Working Group Document), L2/08-030R</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=unicode.org&rft.atitle=Revised+proposal+to+encode+the+decimal+exponent+symbol&rft.date=2008-01-22&rft.aulast=Broukhis&rft.aufirst=Leonid&rft_id=https%3A%2F%2Fwww.unicode.org%2FL2%2FL2008%2F08030r-subscript10.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.unicode.org/versions/Unicode7.0.0/">"The Unicode Standard"</a> (v. 7.0.0 ed.)<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-03-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Unicode+Standard&rft.edition=v.+7.0.0&rft_id=https%3A%2F%2Fwww.unicode.org%2Fversions%2FUnicode7.0.0%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> </p> </span></li> <li id="cite_note-SIMULA_1986-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-SIMULA_1986_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://prosjekt.ring.hibu.no/simula/Standard/chap_1.htm">"SIMULA standard as defined by the SIMULA Standards Group – 3.1 Numbers"</a>. August 1986<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-10-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=SIMULA+standard+as+defined+by+the+SIMULA+Standards+Group+%E2%80%93+3.1+Numbers&rft.date=1986-08&rft_id=http%3A%2F%2Fprosjekt.ring.hibu.no%2Fsimula%2FStandard%2Fchap_1.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-TI_1973_SR-10-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-TI_1973_SR-10_14-0">^</a></b></span> <span class="reference-text">Such as the TI SR-10. <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://www.sliderulemuseum.com/Calculators/SR-10_US.pdf"><i>Texas Instruments electronic slide rule calculator SR-10</i></a> <span class="cs1-format">(PDF)</span>. Dallas: <a href="/wiki/Texas_Instruments_Incorporated" class="mw-redirect" title="Texas Instruments Incorporated">Texas Instruments Incorporated</a>. 1973. 1304-739-266<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-01-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Texas+Instruments+electronic+slide+rule+calculator+SR-10&rft.place=Dallas&rft.pub=Texas+Instruments+Incorporated&rft.date=1973&rft_id=https%3A%2F%2Fwww.sliderulemuseum.com%2FCalculators%2FSR-10_US.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (1+1+45+1 pages) (NB. Although this manual is dated 1973, presumably version 1 of this calculator was introduced in November 1972 according to other sources.)</span> </li> <li id="cite_note-Decapower-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Decapower_15-0">^</a></b></span> <span class="reference-text"> Jim Davidson coined <i>decapower</i> and recommended the "D" separator in the <i><a href="/wiki/65_Notes" class="mw-redirect" title="65 Notes">65 Notes</a></i> newsletter for <a href="/wiki/Hewlett-Packard" title="Hewlett-Packard">Hewlett-Packard</a> <a href="/wiki/HP-65" title="HP-65">HP-65</a> users, and Richard C. Vanderburgh promoted these in the <i><a href="/w/index.php?title=52-Notes&action=edit&redlink=1" class="new" title="52-Notes (page does not exist)">52-Notes</a></i> newsletter for <a href="/wiki/Texas_Instruments" title="Texas Instruments">Texas Instruments</a> <a href="/wiki/SR-52" class="mw-redirect" title="SR-52">SR-52</a> users. <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavidson1976" class="citation journal cs1">Davidson, Jim (January 1976). Nelson, Richard J. (ed.). "[title unknown]". <i><a href="/wiki/65_Notes" class="mw-redirect" title="65 Notes">65 Notes</a></i>. <b>3</b> (1). Santa Ana, CA: 4. V3N1P4.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=65+Notes&rft.atitle=%5Btitle+unknown%5D&rft.volume=3&rft.issue=1&rft.pages=4&rft.date=1976-01&rft.aulast=Davidson&rft.aufirst=Jim&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVanderburgh1976" class="citation journal cs1">Vanderburgh, Richard C., ed. (November 1976). <a rel="nofollow" class="external text" href="http://www.claudiolarini.altervista.org/pdf/52NOTES.pdf">"Decapower"</a> <span class="cs1-format">(PDF)</span>. <i>52-Notes – Newsletter of the SR-52 Users Club</i>. <b>1</b> (6). Dayton, OH: 1. V1N6P1<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-05-28</span></span>. <q><i>Decapower</i> – In the January 1976 issue of <a href="/wiki/65_Notes" class="mw-redirect" title="65 Notes">65-Notes</a> (V3N1p4) Jim Davidson (<a href="/wiki/HP-65" title="HP-65">HP-65</a> Users Club member #547) suggested the term "decapower" as a descriptor for the power-of-ten multiplier used in scientific notation displays. I'm going to begin using it in place of "<a href="/wiki/Exponent" class="mw-redirect" title="Exponent">exponent</a>" which is technically incorrect, and the letter D to separate the "mantissa" from the decapower for typewritten numbers, as Jim also suggests. For example, <code>123<sup>−45</sup></code> [<i><a href="/wiki/Sic" title="Sic">sic</a></i>] which is displayed in scientific notation as <code>1.23 -43</code> will now be written <code>1.23D-43</code>. Perhaps, as this notation gets more and more usage, the calculator manufacturers will change their keyboard abbreviations. HP's EEX and TI's EE could be changed to ED (for enter decapower).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=52-Notes+%E2%80%93+Newsletter+of+the+SR-52+Users+Club&rft.atitle=Decapower&rft.volume=1&rft.issue=6&rft.pages=1&rft.date=1976-11&rft_id=http%3A%2F%2Fwww.claudiolarini.altervista.org%2Fpdf%2F52NOTES.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <a rel="nofollow" class="external autonumber" href="https://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html">[1]</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html">"Decapower"</a>. <i>52-Notes – Newsletter of the SR-52 Users Club</i>. Vol. 1, no. 6. Dayton, OH. November 1976. p. 1<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-05-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=52-Notes+%E2%80%93+Newsletter+of+the+SR-52+Users+Club&rft.atitle=Decapower&rft.volume=1&rft.issue=6&rft.pages=1&rft.date=1976-11&rft_id=http%3A%2F%2Fwww.rskey.org%2FDOCUMENTS%2F52NOTES%2F52v1n6.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (NB. The term <i>decapower</i> was frequently used in subsequent issues of this newsletter up to at least 1978.) </p> </span></li> <li id="cite_note-Sharp-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Sharp_16-0">^</a></b></span> <span class="reference-text"> Specifically, models <a href="/w/index.php?title=Sharp_PC-1280&action=edit&redlink=1" class="new" title="Sharp PC-1280 (page does not exist)">PC-1280</a> (1987), <a href="/w/index.php?title=Sharp_PC-1470U&action=edit&redlink=1" class="new" title="Sharp PC-1470U (page does not exist)">PC-1470U</a> (1987), <a href="/w/index.php?title=Sharp_PC-1475&action=edit&redlink=1" class="new" title="Sharp PC-1475 (page does not exist)">PC-1475</a> (1987), <a href="/wiki/Sharp_PC-1480U" class="mw-redirect" title="Sharp PC-1480U">PC-1480U</a> (1988), <a href="/wiki/Sharp_PC-1490U" class="mw-redirect" title="Sharp PC-1490U">PC-1490U</a> (1990), <a href="/wiki/Sharp_PC-1490UII" class="mw-redirect" title="Sharp PC-1490UII">PC-1490UII</a> (1991), <a href="/wiki/Sharp_PC-E500" class="mw-redirect" title="Sharp PC-E500">PC-E500</a> (1988), <a href="/wiki/Sharp_PC-E500S" title="Sharp PC-E500S">PC-E500S</a> (1995), <a href="/wiki/Sharp_PC-E550" class="mw-redirect" title="Sharp PC-E550">PC-E550</a> (1990), <a href="/wiki/Sharp_PC-E650" class="mw-redirect" title="Sharp PC-E650">PC-E650</a> (1993), and <a href="/wiki/Sharp_PC-U6000" class="mw-redirect" title="Sharp PC-U6000">PC-U6000</a> (1993). <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1280-de.pdf"><i>SHARP Taschencomputer Modell PC-1280 Bedienungsanleitung</i></a> [<i>SHARP Pocket Computer Model PC-1280 Operation Manual</i>] <span class="cs1-format">(PDF)</span> (in German). <a href="/wiki/Sharp_Corporation" title="Sharp Corporation">Sharp Corporation</a>. 1987. pp. 56–60. 7M 0.8-I(TINSG1123ECZZ)(3)<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-03-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=SHARP+Taschencomputer+Modell+PC-1280+Bedienungsanleitung&rft.pages=56-60&rft.pub=Sharp+Corporation&rft.date=1987&rft_id=http%3A%2F%2Fwww.instructionsmanuals.com%2Fu2%2Fpdf%2Fcalculadoras%2FSharp-PC1280-de.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170225090805/http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1475-de.pdf"><i>SHARP Taschencomputer Modell PC-1475 Bedienungsanleitung</i></a> [<i>SHARP Pocket Computer Model PC-1475 Operation Manual</i>] <span class="cs1-format">(PDF)</span> (in German). <a href="/wiki/Sharp_Corporation" title="Sharp Corporation">Sharp Corporation</a>. 1987. pp. 105–108, 131–134, 370, 375. Archived from <a rel="nofollow" class="external text" href="http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1475-de.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2017-02-25<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-02-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=SHARP+Taschencomputer+Modell+PC-1475+Bedienungsanleitung&rft.pages=105-108%2C+131-134%2C+370%2C+375&rft.pub=Sharp+Corporation&rft.date=1987&rft_id=http%3A%2F%2Fwww.instructionsmanuals.com%2Fu2%2Fpdf%2Fcalculadoras%2FSharp-PC1475-de.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>SHARP Pocket Computer Model PC-E500 Operation Manual</i>. <a href="/wiki/Sharp_Corporation" title="Sharp Corporation">Sharp Corporation</a>. 1989. 9G1KS(TINSE1189ECZZ).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=SHARP+Pocket+Computer+Model+PC-E500+Operation+Manual&rft.pub=Sharp+Corporation&rft.date=1989&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170224235944/http://vininc.de/Literatur/Sharp%20Bedienungsanleitungen/PC-E500S-DE.pdf"><i>SHARP Taschencomputer Modell PC-E500S Bedienungsanleitung</i></a> [<i>SHARP Pocket Computer Model PC-E500S Operation Manual</i>] <span class="cs1-format">(PDF)</span> (in German). <a href="/wiki/Sharp_Corporation" title="Sharp Corporation">Sharp Corporation</a>. 1995. 6J3KS(TINSG1223ECZZ). Archived from <a rel="nofollow" class="external text" href="http://vininc.de/Literatur/Sharp%20Bedienungsanleitungen/PC-E500S-DE.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2017-02-24<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-02-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=SHARP+Taschencomputer+Modell+PC-E500S+Bedienungsanleitung&rft.pub=Sharp+Corporation&rft.date=1995&rft_id=http%3A%2F%2Fvininc.de%2FLiteratur%2FSharp%2520Bedienungsanleitungen%2FPC-E500S-DE.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-script cs1-prop-foreign-lang-source"> <bdi lang="ja">電言板5 PC-1490UII PROGRAM LIBRARY</bdi> [<i>Telephone board 5 PC-1490UII program library</i>] (in Japanese). Vol. 5. University Co-op. 1991.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%E9%9B%BB%E8%A8%80%E6%9D%BF5+PC-1490UII+PROGRAM+LIBRARY&rft.pub=University+Co-op&rft.date=1991&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-script cs1-prop-foreign-lang-source"> <bdi lang="ja">電言板6 PC-U6000 PROGRAM LIBRARY</bdi> [<i>Telephone board 6 PC-U6000 program library</i>] (in Japanese). Vol. 6. University Co-op. 1993.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%E9%9B%BB%E8%A8%80%E6%9D%BF6+PC-U6000+PROGRAM+LIBRARY&rft.pub=University+Co-op&rft.date=1993&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> </p> </span></li> <li id="cite_note-TI-83-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-TI-83_17-0">^</a></b></span> <span class="reference-text">Also see <a href="/wiki/TI_calculator_character_sets" title="TI calculator character sets">TI calculator character sets</a>. <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://education.ti.com/downloads/guidebooks/sdk/83p/sdk83pguide.pdf">"TI-83 Programmer's Guide"</a> <span class="cs1-format">(PDF)</span><span class="reference-accessdate">. Retrieved <span class="nowrap">2010-03-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=TI-83+Programmer%27s+Guide&rft_id=http%3A%2F%2Feducation.ti.com%2Fdownloads%2Fguidebooks%2Fsdk%2F83p%2Fsdk83pguide.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> </p> </span></li> <li id="cite_note-Whitaker_1962-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Whitaker_1962_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhitaker1962" class="citation magazine cs1">Whitaker, Ronald O. (1962-06-15). <a rel="nofollow" class="external text" href="http://www.bitsavers.org/magazines/Electronics/Electronics_V35_N24_19620615.pdf">"Numerical Prefixes"</a> <span class="cs1-format">(PDF)</span>. Crosstalk. <i><a href="/wiki/Electronics_(magazine)" title="Electronics (magazine)">Electronics</a></i>. p. 4<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-12-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Electronics&rft.atitle=Numerical+Prefixes&rft.pages=4&rft.date=1962-06-15&rft.aulast=Whitaker&rft.aufirst=Ronald+O.&rft_id=http%3A%2F%2Fwww.bitsavers.org%2Fmagazines%2FElectronics%2FElectronics_V35_N24_19620615.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (1 page)</span> </li> <li id="cite_note-Samples-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Samples_19-0">^</a></b></span> <span class="reference-text">Samples of usage of terminology and variants: <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoller1976" class="citation web cs1">Moller, Donald A. (June 1976). <a rel="nofollow" class="external text" href="http://darchive.mblwhoilibrary.org/bitstream/1912/665/1/WHOI-76-59.pdf">"A Computer Program For The Design And Static Analysis Of Single-Point Sub-Surface Mooring Systems: NOYFB"</a> <span class="cs1-format">(PDF)</span> (Technica Report). WHOI Document Collection. Woods Hole, MA: Woods Hole Oceanographic Institution. WHOI-76-59<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-08-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Computer+Program+For+The+Design+And+Static+Analysis+Of+Single-Point+Sub-Surface+Mooring+Systems%3A+NOYFB&rft.place=Woods+Hole%2C+MA&rft.series=WHOI+Document+Collection&rft.pub=Woods+Hole+Oceanographic+Institution&rft.date=1976-06&rft.aulast=Moller&rft.aufirst=Donald+A.&rft_id=http%3A%2F%2Fdarchive.mblwhoilibrary.org%2Fbitstream%2F1912%2F665%2F1%2FWHOI-76-59.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071019061437/http://brookscole.com/physics_d/templates/student_resources/003026961X_serway/review/expnot.html">"Cengage – the Leading Provider of Higher Education Course Materials"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.brookscole.com/physics_d/templates/student_resources/003026961X_serway/review/expnot.html">the original</a> on 2007-10-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Cengage+%E2%80%93+the+Leading+Provider+of+Higher+Education+Course+Materials&rft_id=http%3A%2F%2Fwww.brookscole.com%2Fphysics_d%2Ftemplates%2Fstudent_resources%2F003026961X_serway%2Freview%2Fexpnot.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.brynmawr.edu/nsf/tutorial/ss/ssnot.html">"Bryn Mawr College: Survival Skills for Problem Solving – Scientific Notation"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-04-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Bryn+Mawr+College%3A+Survival+Skills+for+Problem+Solving+%E2%80%93+Scientific+Notation&rft_id=http%3A%2F%2Fwww.brynmawr.edu%2Fnsf%2Ftutorial%2Fss%2Fssnot.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.lasalle.edu/~smithsc/Astronomy/Units/sci_notation.html">"Scientific Notation"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2007-04-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Scientific+Notation&rft_id=http%3A%2F%2Fwww.lasalle.edu%2F~smithsc%2FAstronomy%2FUnits%2Fsci_notation.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <a rel="nofollow" class="external autonumber" href="https://web.archive.org/web/20061029195358/http://www.gnsphysics.com/mathreview.pdf">[2]</a> <div class="paragraphbreak" style="margin-top:0.5em"></div> <p><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150503005623/http://www.ttinet.com/doc/language_v44_003.html">"INTOUCH 4GL a Guide to the INTOUCH Language"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.ttinet.com/doc/language_v44_003.html#heading_3.2.4.2">the original</a> on 2015-05-03.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=INTOUCH+4GL+a+Guide+to+the+INTOUCH+Language&rft_id=http%3A%2F%2Fwww.ttinet.com%2Fdoc%2Flanguage_v44_003.html%23heading_3.2.4.2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> </p> </span></li> <li id="cite_note-CODATA2014Full-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-CODATA2014Full_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMohrNewellTaylor2016" class="citation journal cs1">Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (July–September 2016). <a rel="nofollow" class="external text" href="http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=920687">"CODATA recommended values of the fundamental physical constants: 2014"</a>. <i><a href="/wiki/Reviews_of_Modern_Physics" title="Reviews of Modern Physics">Reviews of Modern Physics</a></i>. <b>88</b> (3): 035009. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1507.07956">1507.07956</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016RvMP...88c5009M">2016RvMP...88c5009M</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.150.1225">10.1.1.150.1225</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.88.035009">10.1103/RevModPhys.88.035009</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1115862">1115862</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=CODATA+recommended+values+of+the+fundamental+physical+constants%3A+2014&rft.volume=88&rft.issue=3&rft.pages=035009&rft.date=2016-07%2F2016-09&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1115862%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2016RvMP...88c5009M&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.150.1225%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.88.035009&rft_id=info%3Aarxiv%2F1507.07956&rft.aulast=Mohr&rft.aufirst=Peter+J.&rft.au=Newell%2C+David+B.&rft.au=Taylor%2C+Barry+N.&rft_id=http%3A%2F%2Fws680.nist.gov%2Fpublication%2Fget_pdf.cfm%3Fpub_id%3D920687&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Luzum_2011-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Luzum_2011_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLuzumCapitaineFiengaFolkner2011" class="citation journal cs1">Luzum, Brian; Capitaine, Nicole; Fienga, Agnès; Folkner, William; Fukushima, Toshio; Hilton, James; Hohenkerk, Catherine; Krasinsky, George; Petit, Gérard; Pitjeva, Elena; Soffel, Michael; Wallace, Patrick (August 2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10569-011-9352-4">"The IAU 2009 system of astronomical constants: The report of the IAU working group on numerical standards for Fundamental Astronomy"</a>. <i>Celestial Mechanics and Dynamical Astronomy</i>. <b>110</b> (4): 293–304. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011CeMDA.110..293L">2011CeMDA.110..293L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10569-011-9352-4">10.1007/s10569-011-9352-4</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Celestial+Mechanics+and+Dynamical+Astronomy&rft.atitle=The+IAU+2009+system+of+astronomical+constants%3A+The+report+of+the+IAU+working+group+on+numerical+standards+for+Fundamental+Astronomy&rft.volume=110&rft.issue=4&rft.pages=293-304&rft.date=2011-08&rft_id=info%3Adoi%2F10.1007%2Fs10569-011-9352-4&rft_id=info%3Abibcode%2F2011CeMDA.110..293L&rft.aulast=Luzum&rft.aufirst=Brian&rft.au=Capitaine%2C+Nicole&rft.au=Fienga%2C+Agn%C3%A8s&rft.au=Folkner%2C+William&rft.au=Fukushima%2C+Toshio&rft.au=Hilton%2C+James&rft.au=Hohenkerk%2C+Catherine&rft.au=Krasinsky%2C+George&rft.au=Petit%2C+G%C3%A9rard&rft.au=Pitjeva%2C+Elena&rft.au=Soffel%2C+Michael&rft.au=Wallace%2C+Patrick&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs10569-011-9352-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Lide_2000-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lide_2000_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVarious2000" class="citation book cs1">Various (2000). Lide, David R. (ed.). <i>Handbook of Chemistry and Physics</i> (81st ed.). CRC. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8493-0481-1" title="Special:BookSources/978-0-8493-0481-1"><bdi>978-0-8493-0481-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Chemistry+and+Physics&rft.edition=81st&rft.pub=CRC&rft.date=2000&rft.isbn=978-0-8493-0481-1&rft.au=Various&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Kadzere_2008-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kadzere_2008_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKadzere2008" class="citation web cs1">Kadzere, Martin (2008-10-09). <a rel="nofollow" class="external text" href="http://allafrica.com/stories/200810090256.html">"Zimbabwe: Inflation Soars to 231 Million Percent"</a>. Harare, Zimbabwe: <a href="/wiki/The_Herald_(Zimbabwe)" title="The Herald (Zimbabwe)">The Herald</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-10-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Zimbabwe%3A+Inflation+Soars+to+231+Million+Percent&rft.place=Harare%2C+Zimbabwe&rft.pub=The+Herald&rft.date=2008-10-09&rft.aulast=Kadzere&rft.aufirst=Martin&rft_id=http%3A%2F%2Fallafrica.com%2Fstories%2F200810090256.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-BBC-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-BBC_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090514123525/http://news.bbc.co.uk/1/hi/world/africa/7660569.stm">"Zimbabwe inflation hits new high"</a>. <a href="/wiki/BBC_News" title="BBC News">BBC News</a>. 2008-10-09. Archived from <a rel="nofollow" class="external text" href="http://news.bbc.co.uk/1/hi/world/africa/7660569.stm">the original</a> on 2009-05-14<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-10-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Zimbabwe+inflation+hits+new+high&rft.date=2008-10-09&rft_id=http%3A%2F%2Fnews.bbc.co.uk%2F1%2Fhi%2Fworld%2Fafrica%2F7660569.stm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-TI_1974_SR-22-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-TI_1974_SR-22_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://www.datamath.net/Manuals/SR-22_US.pdf"><i>electronic hexadecimal calculator/converter SR-22</i></a> <span class="cs1-format">(PDF)</span> (Revision A ed.). <a href="/wiki/Texas_Instruments_Incorporated" class="mw-redirect" title="Texas Instruments Incorporated">Texas Instruments Incorporated</a>. 1974. p. 7. 1304-389 Rev A<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-03-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=electronic+hexadecimal+calculator%2Fconverter+SR-22&rft.pages=7&rft.edition=Revision+A&rft.pub=Texas+Instruments+Incorporated&rft.date=1974&rft_id=http%3A%2F%2Fwww.datamath.net%2FManuals%2FSR-22_US.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (NB. This calculator supports floating point numbers in scientific notation in bases 8, 10 and 16.)</span> </li> <li id="cite_note-HP16C-Lib-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-HP16C-Lib_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-HP16C-Lib_26-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-HP16C-Lib_26-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-HP16C-Lib_26-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-HP16C-Lib_26-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-HP16C-Lib_26-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartzGrevelle2003" class="citation book cs1">Schwartz, Jake; Grevelle, Rick (2003-10-20) [April 1993]. <a rel="nofollow" class="external text" href="http://www.pahhc.org/mul8r.htm"><i>HP16C Emulator Library for the HP48S/SX</i></a>. 1.20 (1 ed.)<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-08-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=HP16C+Emulator+Library+for+the+HP48S%2FSX&rft.series=1.20&rft.edition=1&rft.date=2003-10-20&rft.aulast=Schwartz&rft.aufirst=Jake&rft.au=Grevelle%2C+Rick&rft_id=http%3A%2F%2Fwww.pahhc.org%2Fmul8r.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span> (NB. This library also works on the <a href="/wiki/HP_48G" class="mw-redirect" title="HP 48G">HP 48G</a>/<a href="/wiki/HP_48GX" class="mw-redirect" title="HP 48GX">GX</a>/<a href="/wiki/HP_48G%2B" class="mw-redirect" title="HP 48G+">G+</a>. Beyond the feature set of the <a href="/wiki/HP-16C" title="HP-16C">HP-16C</a>, this package also supports calculations for binary, octal, and hexadecimal <a href="/wiki/Floating-point_number" class="mw-redirect" title="Floating-point number">floating-point numbers</a> in scientific notation in addition to the usual decimal floating-point numbers.)</span> </li> <li id="cite_note-Martin_1968-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-Martin_1968_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMartin1968" class="citation journal cs1">Martin, Bruce Alan (October 1968). <a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F364096.364107">"Letters to the editor: On binary notation"</a>. <i><a href="/wiki/Communications_of_the_ACM" title="Communications of the ACM">Communications of the ACM</a></i>. <b>11</b> (10): 658. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F364096.364107">10.1145/364096.364107</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:28248410">28248410</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Communications+of+the+ACM&rft.atitle=Letters+to+the+editor%3A+On+binary+notation&rft.volume=11&rft.issue=10&rft.pages=658&rft.date=1968-10&rft_id=info%3Adoi%2F10.1145%2F364096.364107&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A28248410%23id-name%3DS2CID&rft.aulast=Martin&rft.aufirst=Bruce+Alan&rft_id=https%3A%2F%2Fdoi.org%2F10.1145%252F364096.364107&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-HP16C-Add-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-HP16C-Add_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-HP16C-Add_28-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-HP16C-Add_28-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartzGrevelle2003" class="citation book cs1">Schwartz, Jake; Grevelle, Rick (2003-10-21). <a rel="nofollow" class="external text" href="http://www.pahhc.org/mul8r.htm"><i>HP16C Emulator Library for the HP48 – Addendum to the Operator's Manual</i></a>. 1.20 (1 ed.)<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-08-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=HP16C+Emulator+Library+for+the+HP48+%E2%80%93+Addendum+to+the+Operator%27s+Manual&rft.series=1.20&rft.edition=1&rft.date=2003-10-21&rft.aulast=Schwartz&rft.aufirst=Jake&rft.au=Grevelle%2C+Rick&rft_id=http%3A%2F%2Fwww.pahhc.org%2Fmul8r.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Rationale_2003_C-29"><span class="mw-cite-backlink">^ <a href="#cite_ref-Rationale_2003_C_29-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Rationale_2003_C_29-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.open-std.org/jtc1/sc22/wg14/www/C99RationaleV5.10.pdf">"Rationale for International Standard – Programming Languages – C"</a> <span class="cs1-format">(PDF)</span>. 5.10. 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Retrieved <span class="nowrap">2016-06-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Open+Group+Base+Specifications&rft.atitle=dprintf%2C+fprintf%2C+printf%2C+snprintf%2C+sprintf+%E2%80%93+print+formatted+output&rft.date=2013&rft.au=The+IEEE+and+The+Open+Group&rft_id=http%3A%2F%2Fpubs.opengroup.org%2Fonlinepubs%2F9699919799%2Ffunctions%2Fprintf.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Beebe_2017_Hex-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-Beebe_2017_Hex_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeebe2017" class="citation book cs1">Beebe, Nelson H. F. (2017-08-22). <i>The Mathematical-Function Computation Handbook – Programming Using the MathCW Portable Software Library</i> (1 ed.). Salt Lake City: Springer. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-64110-2">10.1007/978-3-319-64110-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-64109-6" title="Special:BookSources/978-3-319-64109-6"><bdi>978-3-319-64109-6</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/2017947446">2017947446</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:30244721">30244721</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical-Function+Computation+Handbook+%E2%80%93+Programming+Using+the+MathCW+Portable+Software+Library&rft.place=Salt+Lake+City&rft.edition=1&rft.pub=Springer&rft.date=2017-08-22&rft_id=info%3Adoi%2F10.1007%2F978-3-319-64110-2&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A30244721%23id-name%3DS2CID&rft_id=info%3Alccn%2F2017947446&rft.isbn=978-3-319-64109-6&rft.aulast=Beebe&rft.aufirst=Nelson+H.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-C++17-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-C++17_32-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://en.cppreference.com/w/cpp/language/floating_literal">"floating point literal"</a>. <i>cppreference.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2017-03-11</span></span>. <q>The hexadecimal floating-point literals were not part of C++ until C++17, although they can be parsed and printed by the I/O functions since C++11: both C++ I/O streams when std::hexfloat is enabled and the C I/O streams: std::printf, std::scanf, etc. See std::strtof for the format description.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=cppreference.com&rft.atitle=floating+point+literal&rft_id=http%3A%2F%2Fen.cppreference.com%2Fw%2Fcpp%2Flanguage%2Ffloating_literal&rfr_id=info%3Asid%2Fen.wikipedia.org%3AScientific+notation" class="Z3988"></span></span> </li> <li id="cite_note-Swift_2017-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-Swift_2017_33-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/LexicalStructure.html">"The Swift Programming Language (Swift 3.0.1)"</a>. <i>Guides and Sample Code: Developer: Language Reference</i>. <a href="/wiki/Apple_Inc." title="Apple Inc.">Apple Corporation</a>. 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