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十进制 - 维基百科,自由的百科全书

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mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&amp;returnto=%E5%8D%81%E8%BF%9B%E5%88%B6" title="建议你登录,尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><!-- CentralNotice --></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-来源" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#来源"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>来源</span> </div> </a> <button aria-controls="toc-来源-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>开关来源子章节</span> </button> <ul id="toc-来源-sublist" class="vector-toc-list"> <li id="toc-世界各国的数字系统" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#世界各国的数字系统"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>世界各国的数字系统</span> </div> </a> <ul id="toc-世界各国的数字系统-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-方法" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#方法"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>方法</span> </div> </a> <button aria-controls="toc-方法-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>开关方法子章节</span> </button> <ul id="toc-方法-sublist" class="vector-toc-list"> <li id="toc-用文字表示十進整數位" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#用文字表示十進整數位"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>用文字表示十進整數位</span> </div> </a> <ul id="toc-用文字表示十進整數位-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-用文字表示十進小數位" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#用文字表示十進小數位"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>用文字表示十進小數位</span> </div> </a> <ul id="toc-用文字表示十進小數位-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-历史沿革" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#历史沿革"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>历史沿革</span> </div> </a> <button aria-controls="toc-历史沿革-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>开关历史沿革子章节</span> </button> <ul id="toc-历史沿革-sublist" class="vector-toc-list"> <li id="toc-起源" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#起源"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>起源</span> </div> </a> <ul id="toc-起源-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-印度与阿拉伯的十进位制" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#印度与阿拉伯的十进位制"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>印度与阿拉伯的十进位制</span> </div> </a> <ul id="toc-印度与阿拉伯的十进位制-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-十进-{制}-與度量衡" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#十进-{制}-與度量衡"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>十进制與度量衡</span> </div> </a> <ul id="toc-十进-{制}-與度量衡-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-清华简算表" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#清华简算表"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>清华简算表</span> </div> </a> <ul id="toc-清华简算表-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參見" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參見"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>參見</span> </div> </a> <ul id="toc-參見-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部連結" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連結"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>外部連結</span> </div> </a> <ul id="toc-外部連結-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="目录" 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="开关目录" > <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">开关目录</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">十进制</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="前往另一种语言写成的文章。86种语言可用" > <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-86" 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">86种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Dezimalsystem" title="Dezimalsystem – 瑞士德语" lang="gsw" hreflang="gsw" data-title="Dezimalsystem" data-language-autonym="Alemannisch" data-language-local-name="瑞士德语" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%A7%D9%85_%D8%B9%D8%AF_%D8%B9%D8%B4%D8%B1%D9%8A" title="نظام عد عشري – 阿拉伯语" lang="ar" hreflang="ar" data-title="نظام عد عشري" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Sistema_de_numberaci%C3%B3n_decimal" title="Sistema de numberación decimal – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Sistema de numberación decimal" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Onluq_sistemi" title="Onluq sistemi – 阿塞拜疆语" lang="az" hreflang="az" data-title="Onluq sistemi" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A3%D0%BD%D0%B0%D1%80%D0%BB%D1%8B_%D0%B8%D2%AB%D3%99%D0%BF%D0%BB%D3%99%D2%AF_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0%D2%BB%D1%8B" title="Унарлы иҫәпләү системаһы – 巴什基尔语" lang="ba" hreflang="ba" data-title="Унарлы иҫәпләү системаһы" data-language-autonym="Башҡортса" data-language-local-name="巴什基尔语" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Desimal" title="Desimal – Central Bikol" lang="bcl" hreflang="bcl" data-title="Desimal" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D0%B7%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Дзесятковая сістэма злічэння – 白俄罗斯语" lang="be" hreflang="be" data-title="Дзесятковая сістэма злічэння" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%94%D0%B7%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%8B%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D1%8C%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D1%8C%D0%BD%D1%8F" title="Дзесятковая сыстэма зьлічэньня – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Дзесятковая сыстэма зьлічэньня" 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%94%D0%B5%D1%81%D0%B5%D1%82%D0%B8%D1%87%D0%BD%D0%B0_%D0%B1%D1%80%D0%BE%D0%B9%D0%BD%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Десетична бройна система – 保加利亚语" lang="bg" hreflang="bg" data-title="Десетична бройна система" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A6%B6%E0%A6%AE%E0%A6%BF%E0%A6%95_%E0%A6%AA%E0%A6%A6%E0%A7%8D%E0%A6%A7%E0%A6%A4%E0%A6%BF" title="দশমিক পদ্ধতি – 孟加拉语" lang="bn" hreflang="bn" data-title="দশমিক পদ্ধতি" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Dispakadur_dekredel" title="Dispakadur dekredel – 布列塔尼语" lang="br" hreflang="br" data-title="Dispakadur dekredel" data-language-autonym="Brezhoneg" data-language-local-name="布列塔尼语" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Dekadni_sistem_brojeva" title="Dekadni sistem brojeva – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Dekadni sistem brojeva" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_decimal" title="Nombre decimal – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Nombre decimal" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AF%DB%95%D8%AF%DB%95%DB%8C%DB%8C" title="دەدەیی – 中库尔德语" lang="ckb" hreflang="ckb" data-title="دەدەیی" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Des%C3%ADtkov%C3%A1_soustava" title="Desítková soustava – 捷克语" lang="cs" hreflang="cs" data-title="Desítková soustava" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%D1%83%D0%BD%D1%88%D0%B0%D1%80%D0%BB%C4%83_%D1%88%D1%83%D1%82_%D1%82%D1%8B%D1%82%C4%83%D0%BC%C4%95" title="Вуншарлă шут тытăмĕ – 楚瓦什语" lang="cv" hreflang="cv" data-title="Вуншарлă шут тытăмĕ" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Degol" title="Degol – 威尔士语" lang="cy" hreflang="cy" data-title="Degol" data-language-autonym="Cymraeg" data-language-local-name="威尔士语" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dezimalsystem" title="Dezimalsystem – 德语" lang="de" hreflang="de" data-title="Dezimalsystem" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B5%CE%BA%CE%B1%CE%B4%CE%B9%CE%BA%CF%8C_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1" title="Δεκαδικό σύστημα – 希腊语" lang="el" hreflang="el" data-title="Δεκαδικό σύστημα" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Decimal" title="Decimal – 英语" lang="en" hreflang="en" data-title="Decimal" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Dekuma_nombrosistemo" title="Dekuma nombrosistemo – 世界语" lang="eo" hreflang="eo" data-title="Dekuma nombrosistemo" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Sistema_de_numeraci%C3%B3n_decimal" title="Sistema de numeración decimal – 西班牙语" lang="es" hreflang="es" data-title="Sistema de numeración decimal" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/K%C3%BCmnends%C3%BCsteem" title="Kümnendsüsteem – 爱沙尼亚语" lang="et" hreflang="et" data-title="Kümnendsüsteem" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki-sistema_hamartar" title="Zenbaki-sistema hamartar – 巴斯克语" lang="eu" hreflang="eu" data-title="Zenbaki-sistema hamartar" data-language-autonym="Euskara" data-language-local-name="巴斯克语" 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/%D8%AF%D9%87%E2%80%8C%D8%AF%D9%87%DB%8C" title="ده‌دهی – 波斯语" lang="fa" hreflang="fa" data-title="ده‌دهی" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kymmenj%C3%A4rjestelm%C3%A4" title="Kymmenjärjestelmä – 芬兰语" lang="fi" hreflang="fi" data-title="Kymmenjärjestelmä" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_d%C3%A9cimal" title="Système décimal – 法语" lang="fr" hreflang="fr" data-title="Système décimal" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/C%C3%B3ras_deach%C3%BAil" title="Córas deachúil – 爱尔兰语" lang="ga" hreflang="ga" data-title="Córas deachúil" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Sistema_de_numeraci%C3%B3n_decimal" title="Sistema de numeración decimal – 加利西亚语" lang="gl" hreflang="gl" data-title="Sistema de numeración decimal" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A9%D7%99%D7%98%D7%94_%D7%94%D7%A2%D7%A9%D7%A8%D7%95%D7%A0%D7%99%D7%AA" title="השיטה העשרונית – 希伯来语" lang="he" hreflang="he" data-title="השיטה העשרונית" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A4%B6%E0%A4%AE%E0%A4%B2%E0%A4%B5_%E0%A4%AA%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%A4%E0%A4%BF" title="दशमलव पद्धति – 印地语" lang="hi" hreflang="hi" data-title="दशमलव पद्धति" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Dekadski_brojevni_sustav" title="Dekadski brojevni sustav – 克罗地亚语" lang="hr" hreflang="hr" data-title="Dekadski brojevni sustav" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Sist%C3%A8m_desimal" title="Sistèm desimal – 海地克里奥尔语" lang="ht" hreflang="ht" data-title="Sistèm desimal" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地克里奥尔语" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%ADzes_sz%C3%A1mrendszer" title="Tízes számrendszer – 匈牙利语" lang="hu" hreflang="hu" data-title="Tízes számrendszer" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sistem_bilangan_desimal" title="Sistem bilangan desimal – 印度尼西亚语" lang="id" hreflang="id" data-title="Sistem bilangan desimal" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Decimala_nombrosistemo" title="Decimala nombrosistemo – 伊多语" lang="io" hreflang="io" data-title="Decimala nombrosistemo" data-language-autonym="Ido" data-language-local-name="伊多语" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Tugakerfi" title="Tugakerfi – 冰岛语" lang="is" hreflang="is" data-title="Tugakerfi" data-language-autonym="Íslenska" data-language-local-name="冰岛语" 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/Sistema_numerico_decimale" title="Sistema numerico decimale – 意大利语" lang="it" hreflang="it" data-title="Sistema numerico decimale" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8D%81%E9%80%B2%E6%B3%95" title="十進法 – 日语" lang="ja" hreflang="ja" data-title="十進法" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Sistem_wilangan_d%C3%A8simal" title="Sistem wilangan dèsimal – 爪哇语" lang="jv" hreflang="jv" data-title="Sistem wilangan dèsimal" data-language-autonym="Jawa" data-language-local-name="爪哇语" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9E%D0%BD%D0%B4%D1%8B%D2%9B_%D1%81%D0%B0%D0%BD%D0%B0%D1%83_%D0%B6%D2%AF%D0%B9%D0%B5%D1%81%D1%96" title="Ондық санау жүйесі – 哈萨克语" lang="kk" hreflang="kk" data-title="Ондық санау жүйесі" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B2%B6%E0%B2%AE%E0%B2%BE%E0%B2%A8_%E0%B2%AA%E0%B2%A6%E0%B3%8D%E0%B2%A7%E0%B2%A4%E0%B2%BF" title="ದಶಮಾನ ಪದ್ಧತಿ – 卡纳达语" lang="kn" hreflang="kn" data-title="ದಶಮಾನ ಪದ್ಧತಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="卡纳达语" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8B%AD%EC%A7%84%EB%B2%95" title="십진법 – 韩语" lang="ko" hreflang="ko" data-title="십진법" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9E%D0%BD%D0%B4%D1%83%D0%BA_%D1%8D%D1%81%D0%B5%D0%BF%D1%82%D3%A9%D3%A9_%D1%82%D1%83%D1%82%D1%83%D0%BC%D1%83" title="Ондук эсептөө тутуму – 柯尔克孜语" lang="ky" hreflang="ky" data-title="Ондук эсептөө тутуму" data-language-autonym="Кыргызча" data-language-local-name="柯尔克孜语" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Systema_numericum_decimale" title="Systema numericum decimale – 拉丁语" lang="la" hreflang="la" data-title="Systema numericum decimale" data-language-autonym="Latina" data-language-local-name="拉丁语" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Sistem_desimal" title="Sistem desimal – 新共同語言" lang="lfn" hreflang="lfn" data-title="Sistem desimal" data-language-autonym="Lingua Franca Nova" data-language-local-name="新共同語言" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/De%C5%A1imtain%C4%97_skai%C4%8Diavimo_sistema" title="Dešimtainė skaičiavimo sistema – 立陶宛语" lang="lt" hreflang="lt" data-title="Dešimtainė skaičiavimo sistema" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Decim%C4%81l%C4%81_skait%C4%AB%C5%A1anas_sist%C4%93ma" title="Decimālā skaitīšanas sistēma – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Decimālā skaitīšanas sistēma" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9B%D1%83%D0%B0%D0%BD_%D1%87%D0%BE%D1%82%D1%80%D0%B0%D0%B4%D0%B0%D0%BC_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B5" title="Луан чотрадам системе – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Луан чотрадам системе" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%B5%D1%81%D0%B5%D1%82%D0%B8%D1%87%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D0%B5%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Десетичен броен систем – 马其顿语" lang="mk" hreflang="mk" data-title="Десетичен броен систем" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A6%E0%B4%B6%E0%B4%BE%E0%B4%82%E0%B4%B6_%E0%B4%B8%E0%B4%AE%E0%B5%8D%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%A6%E0%B4%BE%E0%B4%AF%E0%B4%82" title="ദശാംശ സമ്പ്രദായം – 马拉雅拉姆语" lang="ml" hreflang="ml" data-title="ദശാംശ സമ്പ്രദായം" data-language-autonym="മലയാളം" data-language-local-name="马拉雅拉姆语" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B2%D1%82%D1%8B%D0%BD_%D1%82%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Аравтын тооллын систем – 蒙古语" lang="mn" hreflang="mn" data-title="Аравтын тооллын систем" data-language-autonym="Монгол" data-language-local-name="蒙古语" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Perpuluhan" title="Perpuluhan – 马来语" lang="ms" hreflang="ms" data-title="Perpuluhan" data-language-autonym="Bahasa Melayu" data-language-local-name="马来语" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Sistema_de_numera%C3%A7on_decimal" title="Sistema de numeraçon decimal – 米兰德斯语" lang="mwl" hreflang="mwl" data-title="Sistema de numeraçon decimal" data-language-autonym="Mirandés" data-language-local-name="米兰德斯语" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Decimaal_talstelsel" title="Decimaal talstelsel – 荷兰语" lang="nl" hreflang="nl" data-title="Decimaal talstelsel" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Titalssystemet" title="Titalssystemet – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Titalssystemet" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Titallsystemet" title="Titallsystemet – 书面挪威语" lang="nb" hreflang="nb" data-title="Titallsystemet" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/Letlase_la_lesome" title="Letlase la lesome – 北索托语" lang="nso" hreflang="nso" data-title="Letlase la lesome" data-language-autonym="Sesotho sa Leboa" data-language-local-name="北索托语" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Sist%C3%A8ma_decimal" title="Sistèma decimal – 奥克语" lang="oc" hreflang="oc" data-title="Sistèma decimal" data-language-autonym="Occitan" data-language-local-name="奥克语" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%87%E0%A8%B8%E0%A8%BC%E0%A8%BE%E0%A8%B0%E0%A9%80%E0%A8%86" title="ਇਸ਼ਾਰੀਆ – 旁遮普语" lang="pa" hreflang="pa" data-title="ਇਸ਼ਾਰੀਆ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="旁遮普语" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dziesi%C4%99tny_system_liczbowy" title="Dziesiętny system liczbowy – 波兰语" lang="pl" hreflang="pl" data-title="Dziesiętny system liczbowy" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistema_de_numera%C3%A7%C3%A3o_decimal" title="Sistema de numeração decimal – 葡萄牙语" lang="pt" hreflang="pt" data-title="Sistema de numeração decimal" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Chunkantin_huchha_llika" title="Chunkantin huchha llika – 克丘亚语" lang="qu" hreflang="qu" data-title="Chunkantin huchha llika" data-language-autonym="Runa Simi" data-language-local-name="克丘亚语" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sistem_zecimal" title="Sistem zecimal – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Sistem zecimal" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D1%81%D1%8F%D1%82%D0%B8%D1%87%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%81%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F" title="Десятичная система счисления – 俄语" lang="ru" hreflang="ru" data-title="Десятичная система счисления" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Dekadni_sistem" title="Dekadni sistem – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Dekadni sistem" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Decimal" title="Decimal – Simple English" lang="en-simple" hreflang="en-simple" data-title="Decimal" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Desiatkov%C3%A1_%C4%8D%C3%ADseln%C3%A1_s%C3%BAstava" title="Desiatková číselná sústava – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Desiatková číselná sústava" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Deseti%C5%A1ki_%C5%A1tevilski_sistem" title="Desetiški številski sistem – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Desetiški številski sistem" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Muravanegumi" title="Muravanegumi – 绍纳语" lang="sn" hreflang="sn" data-title="Muravanegumi" data-language-autonym="ChiShona" data-language-local-name="绍纳语" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%B5%D0%BA%D0%B0%D0%B4%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Декадни систем – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Декадни систем" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Decimala_talsystemet" title="Decimala talsystemet – 瑞典语" lang="sv" hreflang="sv" data-title="Decimala talsystemet" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%A4%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%AE%E0%AE%AE%E0%AF%8D" title="பதின்மம் – 泰米尔语" lang="ta" hreflang="ta" data-title="பதின்மம்" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%90%E0%B8%B2%E0%B8%99%E0%B8%AA%E0%B8%B4%E0%B8%9A" title="เลขฐานสิบ – 泰语" lang="th" hreflang="th" data-title="เลขฐานสิบ" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Onlu_say%C4%B1_sistemi" title="Onlu sayı sistemi – 土耳其语" lang="tr" hreflang="tr" data-title="Onlu sayı sistemi" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A3%D0%BD%D0%B0%D1%80%D0%BB%D1%8B_%D0%B8%D1%81%D3%99%D0%BF%D0%BB%D3%99%D2%AF_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0%D1%81%D1%8B" title="Унарлы исәпләү системасы – 鞑靼语" lang="tt" hreflang="tt" data-title="Унарлы исәпләү системасы" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B5%D1%81%D1%8F%D1%82%D0%BA%D0%BE%D0%B2%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F" title="Десяткова система числення – 乌克兰语" lang="uk" hreflang="uk" data-title="Десяткова система числення" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%B9%DB%8C%D8%AF_%D8%A7%D8%B9%D8%B4%D8%A7%D8%B1%DB%8C%DB%81" title="معید اعشاریہ – 乌尔都语" lang="ur" hreflang="ur" data-title="معید اعشاریہ" data-language-autonym="اردو" data-language-local-name="乌尔都语" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_th%E1%BA%ADp_ph%C3%A2n" title="Hệ thập phân – 越南语" lang="vi" hreflang="vi" data-title="Hệ thập phân" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Desimal" title="Desimal – 瓦瑞语" lang="war" hreflang="war" data-title="Desimal" data-language-autonym="Winaray" data-language-local-name="瓦瑞语" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8D%81%E8%BF%9B%E5%88%B6" title="十进制 – 吴语" lang="wuu" hreflang="wuu" data-title="十进制" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-decimal" title="I-decimal – 科萨语" lang="xh" hreflang="xh" data-title="I-decimal" data-language-autonym="IsiXhosa" data-language-local-name="科萨语" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%93%D7%A2%D7%A6%D7%99%D7%9E%D7%90%D7%9C" title="דעצימאל – 意第绪语" lang="yi" hreflang="yi" data-title="דעצימאל" data-language-autonym="ייִדיש" data-language-local-name="意第绪语" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%8D%81%E9%80%B2%E5%88%B6" title="十進制 – 文言文" lang="lzh" hreflang="lzh" data-title="十進制" data-language-autonym="文言" data-language-local-name="文言文" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Si%CC%8Dp-ch%C3%ACn-hoat" title="Si̍p-chìn-hoat – 闽南语" lang="nan" hreflang="nan" data-title="Si̍p-chìn-hoat" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="闽南语" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8D%81%E9%80%B2%E5%88%B6" title="十進制 – 粤语" lang="yue" hreflang="yue" data-title="十進制" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span 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href="/w/index.php?title=Gujarati_numerals&amp;action=edit&amp;redlink=1" class="new" title="Gujarati numerals(页面不存在)">Gujarati</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Gujarati_numerals" class="extiw" title="en:Gujarati numerals"><span lang="en" dir="auto">Gujarati numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%8F%A4%E6%9C%A8%E5%9F%BA%E6%96%87" title="古木基文">古木基文</a></li> <li><span class="ilh-all" data-orig-title="Odia numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Odia numerals"><span class="ilh-page"><a href="/w/index.php?title=Odia_numerals&amp;action=edit&amp;redlink=1" class="new" title="Odia numerals(页面不存在)">Odia</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Odia_numerals" class="extiw" title="en:Odia numerals"><span lang="en" dir="auto">Odia numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Sinhala numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Sinhala numerals"><span class="ilh-page"><a href="/w/index.php?title=Sinhala_numerals&amp;action=edit&amp;redlink=1" class="new" title="Sinhala numerals(页面不存在)">Sinhala</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Sinhala_numerals" class="extiw" title="en:Sinhala numerals"><span lang="en" dir="auto">Sinhala numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Tamil numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tamil numerals"><span class="ilh-page"><a href="/w/index.php?title=Tamil_numerals&amp;action=edit&amp;redlink=1" class="new" title="Tamil numerals(页面不存在)">Tamil</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tamil_numerals" class="extiw" title="en:Tamil numerals"><span lang="en" dir="auto">Tamil numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Malayalam numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Malayalam numerals"><span class="ilh-page"><a href="/w/index.php?title=Malayalam_numerals&amp;action=edit&amp;redlink=1" class="new" title="Malayalam numerals(页面不存在)">Malayalam</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Malayalam_numerals" class="extiw" title="en:Malayalam numerals"><span lang="en" dir="auto">Malayalam numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E6%B3%B0%E5%8D%A2%E5%9B%BA%E6%96%87" title="泰卢固文">泰卢固文</a></li> <li><a href="/wiki/%E5%8D%A1%E7%B4%8D%E9%81%94%E6%96%87" title="卡納達文">卡納達文</a></li> <li><span class="ilh-all" data-orig-title="Dzongkha numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Dzongkha numerals"><span class="ilh-page"><a href="/w/index.php?title=Dzongkha_numerals&amp;action=edit&amp;redlink=1" class="new" title="Dzongkha numerals(页面不存在)">Dzongkha</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Dzongkha_numerals" class="extiw" title="en:Dzongkha numerals"><span lang="en" dir="auto">Dzongkha numerals</span></a></span>)</span></span></li></ul> <hr /> <ul><li><span class="ilh-all" data-orig-title="Tibetan numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tibetan numerals"><span class="ilh-page"><a href="/w/index.php?title=Tibetan_numerals&amp;action=edit&amp;redlink=1" class="new" title="Tibetan numerals(页面不存在)">Tibetan</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tibetan_numerals" class="extiw" title="en:Tibetan numerals"><span lang="en" dir="auto">Tibetan numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Balinese numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Balinese numerals"><span class="ilh-page"><a href="/w/index.php?title=Balinese_numerals&amp;action=edit&amp;redlink=1" class="new" title="Balinese numerals(页面不存在)">Balinese</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Balinese_numerals" class="extiw" title="en:Balinese numerals"><span lang="en" dir="auto">Balinese numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E7%B7%AC%E7%94%B8%E6%95%B8%E5%AD%97" title="緬甸數字">緬甸數字</a></li> <li><span class="ilh-all" data-orig-title="Javanese numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Javanese numerals"><span class="ilh-page"><a href="/w/index.php?title=Javanese_numerals&amp;action=edit&amp;redlink=1" class="new" title="Javanese numerals(页面不存在)">Javanese</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Javanese_numerals" class="extiw" title="en:Javanese numerals"><span lang="en" dir="auto">Javanese numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E9%AB%98%E6%A3%89%E6%95%B8%E5%AD%97" title="高棉數字">高棉數字</a></li> <li><a href="/wiki/%E8%80%81%E6%92%BE%E6%96%87" title="老撾文">老撾文</a></li> <li><span class="ilh-all" data-orig-title="Mongolian numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mongolian numerals"><span class="ilh-page"><a href="/w/index.php?title=Mongolian_numerals&amp;action=edit&amp;redlink=1" class="new" title="Mongolian numerals(页面不存在)">Mongolian</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mongolian_numerals" class="extiw" title="en:Mongolian numerals"><span lang="en" dir="auto">Mongolian numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Sundanese numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Sundanese numerals"><span class="ilh-page"><a href="/w/index.php?title=Sundanese_numerals&amp;action=edit&amp;redlink=1" class="new" title="Sundanese numerals(页面不存在)">Sundanese</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Sundanese_numerals" class="extiw" title="en:Sundanese numerals"><span lang="en" dir="auto">Sundanese numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E6%B3%B0%E6%96%87%E6%95%B0%E5%AD%97" title="泰文数字">泰文数字</a></li></ul> <hr /></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><div class="sidebar-list-title-c">東亞體系</div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>當代</dt></dl> <ul><li><a href="/wiki/%E6%B1%89%E5%AD%97%E6%95%B0%E5%AD%97" title="汉字数字">中文数字</a> <ul><li><a href="/wiki/%E8%8B%8F%E5%B7%9E%E7%A0%81%E5%AD%90" title="苏州码子">苏州码子</a></li></ul></li> <li><span class="ilh-all" data-orig-title="閩南語數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Hokkien numerals"><span class="ilh-page"><a href="/w/index.php?title=%E9%96%A9%E5%8D%97%E8%AA%9E%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="閩南語數字(页面不存在)">閩南語數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Hokkien_numerals" class="extiw" title="en:Hokkien numerals"><span lang="en" dir="auto">Hokkien numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E6%97%A5%E8%AA%9E%E6%95%B8%E5%AD%97" title="日語數字">日語數字</a></li> <li><a href="/wiki/%E9%9F%93%E8%AA%9E%E6%95%B8%E5%AD%97" title="韓語數字">韓語數字</a></li> <li><a href="/wiki/%E8%B6%8A%E5%8D%97%E8%AF%AD%E6%95%B0%E5%AD%97" title="越南语数字">越南语数字</a></li></ul> <hr /> <dl><dt>古代</dt></dl> <ul><li><a href="/wiki/%E7%AE%97%E7%AD%B9" title="算筹">算筹</a></li> <li><span class="ilh-all" data-orig-title="西夏數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tangut numerals"><span class="ilh-page"><a href="/w/index.php?title=%E8%A5%BF%E5%A4%8F%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="西夏數字(页面不存在)">西夏數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tangut_numerals" class="extiw" title="en:Tangut numerals"><span lang="en" dir="auto">Tangut numerals</span></a></span>)</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><div class="sidebar-list-title-c">美洲體系</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/%E7%8E%9B%E9%9B%85%E6%95%B0%E5%AD%97" title="玛雅数字">玛雅数字</a></li> <li><span class="ilh-all" data-orig-title="穆伊斯卡數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Muisca numerals"><span class="ilh-page"><a href="/w/index.php?title=%E7%A9%86%E4%BC%8A%E6%96%AF%E5%8D%A1%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="穆伊斯卡數字(页面不存在)">穆伊斯卡數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Muisca_numerals" class="extiw" title="en:Muisca numerals"><span lang="en" dir="auto">Muisca numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%A5%87%E6%99%AE" title="奇普">奇普</a></li></ul> ...</div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><div class="sidebar-list-title-c">其它體系</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><span class="ilh-all" data-orig-title="古數制史" data-lang-code="en" data-lang-name="英语" data-foreign-title="History of ancient numeral systems"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%A4%E6%95%B8%E5%88%B6%E5%8F%B2&amp;action=edit&amp;redlink=1" class="new" title="古數制史(页面不存在)">古數制史</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/History_of_ancient_numeral_systems" class="extiw" title="en:History of ancient numeral systems"><span lang="en" dir="auto">History of ancient numeral systems</span></a></span>)</span></span></li></ul> <hr /> <dl><dt><a href="/wiki/%E5%8F%A4%E4%BB%A3%E5%8F%B2" title="古代史">古代史</a></dt></dl> <ul><li><a href="/wiki/%E5%B7%B4%E6%AF%94%E4%BC%A6%E6%95%B0%E5%AD%97" title="巴比伦数字">巴比伦数字</a></li></ul> <hr /> <dl><dt><a href="/wiki/%E5%90%8E%E5%8F%A4%E4%BB%A3%E5%8F%B2" title="后古代史">後古典</a></dt></dl> <ul><li><span class="ilh-all" data-orig-title="西多會數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Cistercian numerals"><span class="ilh-page"><a href="/w/index.php?title=%E8%A5%BF%E5%A4%9A%E6%9C%83%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="西多會數字(页面不存在)">西多會數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Cistercian_numerals" class="extiw" title="en:Cistercian numerals"><span lang="en" dir="auto">Cistercian numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E7%8E%9B%E9%9B%85%E6%95%B0%E5%AD%97" title="玛雅数字">玛雅数字</a></li> <li><span class="ilh-all" data-orig-title="穆伊斯卡數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Muisca numerals"><span class="ilh-page"><a href="/w/index.php?title=%E7%A9%86%E4%BC%8A%E6%96%AF%E5%8D%A1%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="穆伊斯卡數字(页面不存在)">穆伊斯卡數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Muisca_numerals" class="extiw" title="en:Muisca numerals"><span lang="en" dir="auto">Muisca numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="納維亞五元數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Pentadic numerals"><span class="ilh-page"><a href="/w/index.php?title=%E7%B4%8D%E7%B6%AD%E4%BA%9E%E4%BA%94%E5%85%83%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="納維亞五元數字(页面不存在)">納維亞五元數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Pentadic_numerals" class="extiw" title="en:Pentadic numerals"><span lang="en" dir="auto">Pentadic numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%A5%87%E6%99%AE" title="奇普">奇普</a></li> <li><span class="ilh-all" data-orig-title="魯米數字符號" data-lang-code="en" data-lang-name="英语" data-foreign-title="Rumi Numeral Symbols"><span class="ilh-page"><a href="/w/index.php?title=%E9%AD%AF%E7%B1%B3%E6%95%B8%E5%AD%97%E7%AC%A6%E8%99%9F&amp;action=edit&amp;redlink=1" class="new" title="魯米數字符號(页面不存在)">魯米數字符號</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Rumi_Numeral_Symbols" class="extiw" title="en:Rumi Numeral Symbols"><span lang="en" dir="auto">Rumi Numeral Symbols</span></a></span>)</span></span></li></ul> <hr /> <dl><dt>當代</dt></dl> <ul><li><a href="/wiki/%E5%88%87%E7%BD%97%E5%9F%BA%E9%9F%B3%E8%8A%82%E6%96%87%E5%AD%97" title="切罗基音节文字">切罗基音节文字</a></li> <li><a href="/wiki/%E5%8D%A1%E5%85%8B%E6%89%98%E7%BB%B4%E5%85%8B%E6%95%B0%E5%AD%97" title="卡克托维克数字">卡克托维克数字</a>(Iñupiaq)</li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><div class="sidebar-list-title-c">各<a href="/wiki/%E5%BA%95%E6%95%B0_(%E8%BF%9B%E5%88%B6)" title="底数 (进制)">底數</a>的<a href="/wiki/%E9%80%B2%E4%BD%8D%E5%88%B6" class="mw-redirect" title="進位制">進位制</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>一般進位</dt></dl> <ul><li><a href="/wiki/%E4%BA%8C%E8%BF%9B%E5%88%B6" title="二进制">二进制</a></li> <li><a href="/wiki/%E4%B8%89%E8%BF%9B%E5%88%B6" title="三进制">三进制</a></li> <li><a href="/wiki/%E5%9B%9B%E9%80%B2%E5%88%B6" title="四進制">四進制</a></li> <li><a href="/wiki/%E4%BA%94%E9%80%B2%E5%88%B6" title="五進制">五進制</a></li> <li><a href="/wiki/%E5%85%AD%E8%BF%9B%E5%88%B6" title="六进制">六进制</a></li> <li><a href="/wiki/%E5%85%AB%E8%BF%9B%E5%88%B6" title="八进制">八进制</a></li> <li><a href="/wiki/%E4%B9%9D%E9%80%B2%E4%BD%8D" title="九進位">九進位</a></li> <li><a class="mw-selflink selflink">十进制</a></li> <li><a href="/wiki/%E5%8D%81%E4%B8%80%E8%BF%9B%E5%88%B6" title="十一进制">十一進制</a></li> <li><a href="/wiki/%E5%8D%81%E4%BA%8C%E8%BF%9B%E5%88%B6" title="十二进制">十二进制</a></li> <li><a href="/wiki/%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" title="十六进制">十六进制</a></li> <li><a href="/wiki/%E4%BA%8C%E5%8D%81%E8%BF%9B%E5%88%B6" title="二十进制">二十进制</a></li> <li><a href="/wiki/%E4%B8%89%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" title="三十六进制">三十六進制</a></li> <li><a href="/wiki/%E5%85%AD%E5%8D%81%E9%80%B2%E5%88%B6" title="六十進制">六十進制</a></li> <li><a href="/wiki/%E9%80%B2%E5%88%B6%E8%A1%A8" title="進制表">進制表</a></li></ul> <hr /> <dl><dt><a href="/wiki/%E5%B9%BF%E4%B9%89%E7%9A%84%E8%BF%9B%E5%88%B6%E7%B3%BB%E7%BB%9F" title="广义的进制系统">广义的进制系统</a></dt></dl> <ul><li><a href="/wiki/%E9%9B%99%E5%B0%84%E8%A8%98%E6%95%B8" title="雙射記數">雙射記數</a><span class="nowrap">&#160;</span>(<a href="/wiki/%E4%B8%80%E8%BF%9B%E5%88%B6" title="一进制">一进制</a>)</li> <li><span class="ilh-all" data-orig-title="有符號記數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Signed-digit representation"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%89%E7%AC%A6%E8%99%9F%E8%A8%98%E6%95%B8&amp;action=edit&amp;redlink=1" class="new" title="有符號記數(页面不存在)">有符號記數</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Signed-digit_representation" class="extiw" title="en:Signed-digit representation"><span lang="en" dir="auto">Signed-digit representation</span></a></span>)</span></span><span class="nowrap">&#160;</span>(<a href="/wiki/%E5%B9%B3%E8%A1%A1%E4%B8%89%E9%80%B2%E4%BD%8D" title="平衡三進位">平衡三進位</a>)</li> <li><span class="ilh-all" data-orig-title="混合進制" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mixed radix"><span class="ilh-page"><a href="/w/index.php?title=%E6%B7%B7%E5%90%88%E9%80%B2%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="混合進制(页面不存在)">混合進制</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mixed_radix" class="extiw" title="en:Mixed radix"><span lang="en" dir="auto">Mixed radix</span></a></span>)</span></span><span class="nowrap">&#160;</span>(<a href="/wiki/%E9%98%B6%E4%B9%98%E8%BF%9B%E5%88%B6" title="阶乘进制">阶乘进制</a>)</li> <li><span class="ilh-all" data-orig-title="負進制" data-lang-code="en" data-lang-name="英语" data-foreign-title="Negative base"><span class="ilh-page"><a href="/w/index.php?title=%E8%B2%A0%E9%80%B2%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="負進制(页面不存在)">負進制</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Negative_base" class="extiw" title="en:Negative base"><span lang="en" dir="auto">Negative base</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%A4%8D%E5%BA%95%E6%95%B0%E8%BF%9B%E5%88%B6" title="复底数进制">复底数进制</a><span class="nowrap">&#160;</span>(<a href="/wiki/2i%E9%80%B2%E5%88%B6" title="2i進制">2i進制</a>)</li> <li><a href="/wiki/%E9%9D%9E%E6%95%B4%E6%95%B0%E8%BF%9B%E4%BD%8D%E5%88%B6" title="非整数进位制">非整数进位制</a><span class="nowrap">&#160;</span>(<a href="/wiki/%E9%BB%84%E9%87%91%E8%BF%9B%E5%88%B6" title="黄金进制">黄金进制</a>)</li> <li><span class="ilh-all" data-orig-title="非對稱進制" data-lang-code="en" data-lang-name="英语" data-foreign-title="Asymmetric numeral systems"><span class="ilh-page"><a href="/w/index.php?title=%E9%9D%9E%E5%B0%8D%E7%A8%B1%E9%80%B2%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="非對稱進制(页面不存在)">非對稱進制</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Asymmetric_numeral_systems" class="extiw" title="en:Asymmetric numeral systems"><span lang="en" dir="auto">Asymmetric numeral systems</span></a></span>)</span></span></li></ul></div></div></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title"><div class="sidebar-list-title-c"><a href="/wiki/%E7%AC%A6%E5%80%BC%E7%9B%B8%E5%8A%A0%E8%A8%98%E6%95%B8%E6%B3%95" title="符值相加記數法">符值相加記數法</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>非字母</dt></dl> <ul><li><a href="/wiki/%E6%84%9B%E7%90%B4%E6%95%B8%E5%AD%97" title="愛琴數字">愛琴數字</a></li> <li><a href="/wiki/%E9%98%BF%E6%8F%90%E5%8D%A1%E6%95%B8%E5%AD%97" title="阿提卡數字">阿提卡數字</a></li> <li><a href="/wiki/%E9%98%BF%E8%8C%B2%E7%89%B9%E5%85%8B%E6%96%87%E5%AD%97" title="阿茲特克文字">阿茲特克文字</a></li> <li><span class="ilh-all" data-orig-title="婆羅米數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Brahmi numerals"><span class="ilh-page"><a href="/w/index.php?title=%E5%A9%86%E7%BE%85%E7%B1%B3%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="婆羅米數字(页面不存在)">婆羅米數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Brahmi_numerals" class="extiw" title="en:Brahmi numerals"><span lang="en" dir="auto">Brahmi numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="楚瓦什數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Chuvash numerals"><span class="ilh-page"><a href="/w/index.php?title=%E6%A5%9A%E7%93%A6%E4%BB%80%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="楚瓦什數字(页面不存在)">楚瓦什數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Chuvash_numerals" class="extiw" title="en:Chuvash numerals"><span lang="en" dir="auto">Chuvash numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%8F%A4%E5%9F%83%E5%8F%8A%E6%95%B0%E5%AD%97" title="古埃及数字">古埃及数字</a></li> <li><span class="ilh-all" data-orig-title="伊特拉斯坎數字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Etruscan numerals"><span class="ilh-page"><a href="/w/index.php?title=%E4%BC%8A%E7%89%B9%E6%8B%89%E6%96%AF%E5%9D%8E%E6%95%B8%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="伊特拉斯坎數字(页面不存在)">伊特拉斯坎數字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Etruscan_numerals" class="extiw" title="en:Etruscan numerals"><span lang="en" dir="auto">Etruscan numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E4%BD%89%E5%8D%A2%E6%96%87" title="佉卢文">佉卢文</a></li> <li><span class="ilh-all" data-orig-title="史前計數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Prehistoric counting"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%B2%E5%89%8D%E8%A8%88%E6%95%B8&amp;action=edit&amp;redlink=1" class="new" title="史前計數(页面不存在)">史前計數</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Prehistoric_counting" class="extiw" title="en:Prehistoric counting"><span lang="en" dir="auto">Prehistoric counting</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="原始楔形文字" data-lang-code="en" data-lang-name="英语" data-foreign-title="Proto-cuneiform"><span class="ilh-page"><a href="/w/index.php?title=%E5%8E%9F%E5%A7%8B%E6%A5%94%E5%BD%A2%E6%96%87%E5%AD%97&amp;action=edit&amp;redlink=1" class="new" title="原始楔形文字(页面不存在)">原始楔形文字</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Proto-cuneiform" class="extiw" title="en:Proto-cuneiform"><span lang="en" dir="auto">Proto-cuneiform</span></a></span>)</span></span></li> <li><a href="/wiki/%E7%BD%97%E9%A9%AC%E6%95%B0%E5%AD%97" title="罗马数字">罗马数字</a></li> <li><a href="/wiki/%E8%AE%A1%E6%95%B0%E7%AC%A6%E5%8F%B7" title="计数符号">计数符号</a></li></ul> <hr /> <dl><dt><span class="ilh-all" data-orig-title="字母數制" data-lang-code="en" data-lang-name="英语" data-foreign-title="Alphabetic numeral system"><span class="ilh-page"><a href="/w/index.php?title=%E5%AD%97%E6%AF%8D%E6%95%B8%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="字母數制(页面不存在)">字母數制</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Alphabetic_numeral_system" class="extiw" title="en:Alphabetic numeral system"><span lang="en" dir="auto">Alphabetic numeral system</span></a></span>)</span></span></dt></dl> <ul><li><span class="ilh-all" data-orig-title="Abjad numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Abjad numerals"><span class="ilh-page"><a href="/w/index.php?title=Abjad_numerals&amp;action=edit&amp;redlink=1" class="new" title="Abjad numerals(页面不存在)">Abjad</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Abjad_numerals" class="extiw" title="en:Abjad numerals"><span lang="en" dir="auto">Abjad numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E4%BA%9A%E7%BE%8E%E5%B0%BC%E4%BA%9A%E6%95%B0%E5%AD%97" title="亚美尼亚数字">亚美尼亚数字</a></li> <li><span class="ilh-all" data-orig-title="Alphasyllabic numeral system" data-lang-code="en" data-lang-name="英语" data-foreign-title="Alphasyllabic numeral system"><span class="ilh-page"><a href="/w/index.php?title=Alphasyllabic_numeral_system&amp;action=edit&amp;redlink=1" class="new" title="Alphasyllabic numeral system(页面不存在)">Alphasyllabic</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Alphasyllabic_numeral_system" class="extiw" title="en:Alphasyllabic numeral system"><span lang="en" dir="auto">Alphasyllabic numeral system</span></a></span>)</span></span> <ul><li><span class="ilh-all" data-orig-title="Aksharapalli" data-lang-code="en" data-lang-name="英语" data-foreign-title="Aksharapalli"><span class="ilh-page"><a href="/w/index.php?title=Aksharapalli&amp;action=edit&amp;redlink=1" class="new" title="Aksharapalli(页面不存在)">Akṣarapallī</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Aksharapalli" class="extiw" title="en:Aksharapalli"><span lang="en" dir="auto">Aksharapalli</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Āryabhaṭa numeration" data-lang-code="en" data-lang-name="英语" data-foreign-title="Āryabhaṭa numeration"><span class="ilh-page"><a href="/w/index.php?title=%C4%80ryabha%E1%B9%ADa_numeration&amp;action=edit&amp;redlink=1" class="new" title="Āryabhaṭa numeration(页面不存在)">Āryabhaṭa</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%ADa_numeration" class="extiw" title="en:Āryabhaṭa numeration"><span lang="en" dir="auto">Āryabhaṭa numeration</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Katapayadi system" data-lang-code="en" data-lang-name="英语" data-foreign-title="Katapayadi system"><span class="ilh-page"><a href="/w/index.php?title=Katapayadi_system&amp;action=edit&amp;redlink=1" class="new" title="Katapayadi system(页面不存在)">Kaṭapayādi</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Katapayadi_system" class="extiw" title="en:Katapayadi system"><span lang="en" dir="auto">Katapayadi system</span></a></span>)</span></span></li></ul></li> <li><a href="/wiki/%E7%A7%91%E6%99%AE%E7%89%B9%E5%AD%97%E6%AF%8D" title="科普特字母">科普特字母</a></li> <li><a href="/wiki/%E8%A5%BF%E9%87%8C%E7%88%BE%E6%95%B8%E5%AD%97" title="西里爾數字">西里爾數字</a></li> <li><a href="/wiki/%E5%90%89%E8%8C%B2%E5%AD%97%E6%AF%8D" title="吉茲字母">吉茲字母</a></li> <li><span class="ilh-all" data-orig-title="Georgian numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Georgian numerals"><span class="ilh-page"><a href="/w/index.php?title=Georgian_numerals&amp;action=edit&amp;redlink=1" class="new" title="Georgian numerals(页面不存在)">Georgian</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Georgian_numerals" class="extiw" title="en:Georgian numerals"><span lang="en" dir="auto">Georgian numerals</span></a></span>)</span></span></li> <li><span class="ilh-all" data-orig-title="Glagolitic_numerals" data-lang-code="en" data-lang-name="英语" data-foreign-title="Glagolitic_numerals"><span class="ilh-page"><a href="/w/index.php?title=Glagolitic_numerals&amp;action=edit&amp;redlink=1" class="new" title="Glagolitic numerals(页面不存在)">Glagolitic</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Glagolitic_numerals" class="extiw" title="en:Glagolitic numerals"><span lang="en" dir="auto">Glagolitic_numerals</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%B8%8C%E8%85%8A%E6%95%B0%E5%AD%97" title="希腊数字">希腊数字</a></li> <li><a href="/wiki/%E5%B8%8C%E4%BC%AF%E4%BE%86%E6%95%B8%E5%AD%97" title="希伯來數字">希伯來數字</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <span class="ilh-all" data-orig-title="數制列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of numeral systems"><span class="ilh-page"><a href="/w/index.php?title=%E6%95%B8%E5%88%B6%E5%88%97%E8%A1%A8&amp;action=edit&amp;redlink=1" class="new" title="數制列表(页面不存在)">數制列表</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/List_of_numeral_systems" class="extiw" title="en:List of numeral systems"><span lang="en" dir="auto">List of numeral systems</span></a></span>)</span></span></td></tr><tr><td class="sidebar-navbar" style="line-height:1.6"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ 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href="/w/index.php?title=Template_talk:%E8%AE%B0%E6%95%B0%E7%B3%BB%E7%BB%9F&amp;action=edit&amp;redlink=1" class="new" title="Template talk:记数系统(页面不存在)"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E8%AE%B0%E6%95%B0%E7%B3%BB%E7%BB%9F" title="Special:编辑页面/Template:记数系统"><abbr title="编辑该模板">编</abbr></a></li></ul></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r84833064">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Wikipedia:%E6%B6%88%E6%AD%A7%E4%B9%89" title="Wikipedia:消歧义"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/25px-Disambig_gray.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/38px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/50px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a></span><style data-mw-deduplicate="TemplateStyles:r74069148">body:not(.skin-minerva) .mw-parser-output .ifmobile>.mobile{display:none}body.skin-minerva .mw-parser-output .ifmobile>.nomobile{display:inherit;display:initial}</style><span class="ifmobile"><span class="nomobile">&#160;&#160;</span><span class="mobile"></span></span>关于香港稱為「十進制」的度量衡制度,請見「<b><a href="/wiki/%E7%B1%B3%E5%88%B6" class="mw-redirect" title="米制">米制</a></b>」。</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Rodnumberwithzero.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Rodnumberwithzero.jpg/300px-Rodnumberwithzero.jpg" decoding="async" width="300" height="211" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Rodnumberwithzero.jpg/450px-Rodnumberwithzero.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Rodnumberwithzero.jpg/600px-Rodnumberwithzero.jpg 2x" data-file-width="707" data-file-height="498" /></a><figcaption><a href="/wiki/%E7%AD%B9%E7%AE%97" title="筹算">筹算</a>广泛运用十进位制,其中以空位代表零</figcaption></figure> <p><b>十進制</b>是以<a href="/wiki/10" title="10">10</a>爲<a href="/wiki/%E5%BA%95%E6%95%B0_(%E8%BF%9B%E5%88%B6)" title="底数 (进制)">底数</a>的<a href="/wiki/%E6%95%B0%E5%AD%97%E7%B3%BB%E7%BB%9F" class="mw-disambig" title="数字系统">數字系统</a>,是在世界上應用最廣泛的進位制。 </p><p>十進制有两大类: </p> <ul><li>无位值概念的十進制:<a href="/wiki/%E5%8F%A4%E5%B8%8C%E8%85%8A" title="古希腊">古希腊</a>、<a href="/wiki/%E5%8F%A4%E5%9F%83%E5%8F%8A" title="古埃及">古埃及</a>和<a href="/wiki/%E5%8F%A4%E5%8D%B0%E5%BA%A6" class="mw-redirect" title="古印度">古印度</a>的佉卢十进制和婆羅米十进制都属于这一类。</li> <li>具有<b>位</b>值(place value)概念的十進制,称为「十进<b>位</b>制」,如<a href="/wiki/%E4%B8%AD%E5%9C%8B%E5%8F%A4%E4%BB%A3" class="mw-redirect" title="中國古代">中国古代</a>的算筹数,和<a href="/wiki/%E5%8D%B0%E5%BA%A6%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B0%E5%AD%97" class="mw-redirect" title="印度阿拉伯数字">印度阿拉伯数字</a>,以及现代数学广泛使用的,由印度-阿拉伯数字发展而来的<a href="/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B0%E5%AD%97" title="阿拉伯数字">阿拉伯数字</a>。</li></ul> <p>「十進制」與「十进<b>位</b>制」不同,十進制包括十進位制。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="来源"><span id=".E6.9D.A5.E6.BA.90"></span>来源</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=1" title="编辑章节:来源"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E4%BA%BA%E9%A1%9E" title="人類">人類</a><a href="/wiki/%E7%AE%97%E6%95%B8" class="mw-redirect" title="算數">算數</a>採用十進制,可能跟<a href="/wiki/%E4%BA%BA%E9%A1%9E" title="人類">人類</a>有十根<a href="/wiki/%E6%89%8B%E6%8C%87" title="手指">手指</a>有關。<a href="/wiki/%E4%BA%9A%E9%87%8C%E5%A3%AB%E5%A4%9A%E5%BE%B7" title="亚里士多德">亚里士多德</a>称人类普遍使用十進制,只不过是绝大多数人生来就有10根手指这样一个解剖学事实的结果。实际上,在古代世界独立开发的有文字的记数体系中,除了<a href="/w/index.php?title=%E5%B7%B4%E6%AF%94%E4%BC%A6%E6%96%87%E6%98%8E&amp;action=edit&amp;redlink=1" class="new" title="巴比伦文明(页面不存在)">巴比伦文明</a>的楔形数字为60進制,<a href="/wiki/%E7%8E%9B%E9%9B%85" class="mw-disambig" title="玛雅">玛雅</a>数字为20進制外,几乎全部为十進制。只不过,这些十進制记数体系并不是按位的,沒有位值這個概念。<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="世界各国的数字系统"><span id=".E4.B8.96.E7.95.8C.E5.90.84.E5.9B.BD.E7.9A.84.E6.95.B0.E5.AD.97.E7.B3.BB.E7.BB.9F"></span>世界各国的数字系统</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=2" title="编辑章节:世界各国的数字系统"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>无位值十進制</dt></dl> <ul><li><a href="/wiki/%E5%8F%A4%E5%9F%83%E5%8F%8A" title="古埃及">古埃及</a>十進制:以一个竖道代表1,二并排竖道代表2,三竖道代表3,一横道代表4,左二撇右竖道代表5,上三撇下三撇代表6,上下两道代表8,四个「(」并排代表9,一个“人”字形代表10,“人”上加一横代表20,20左加一点代表30,横道上加一点代表40,横道上加三竖道(如中国筹算的8)代表60,横道上加四竖道代表80(形同中国筹算中的9)代表80,两横道上加三竖代表90……。</li> <li><a href="/wiki/%E5%8F%A4%E5%B8%8C%E8%85%8A" title="古希腊">古希腊</a>十進制,1至9,10至90,100至900各有不同的单字母代表。</li> <li>古印度Kharosshi十進制,以一个竖道代表1,二并排竖道代表2,三竖道代表3,一个X代表4,IX代表5,||X代表6,XX代表8,10,20个有单字符代表。</li> <li>古印度和Brahmi十進制,和希腊十進制相似,1至9,10至90,100至900各有不同的单字母代表。符号很多。</li></ul> <dl><dt><style data-mw-deduplicate="TemplateStyles:r79700083">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}</style><span class="vanchor"><span class="anchor" id="十进位制"></span><span class="anchor" id="有位值十進制"></span><span class="vanchor-text">十进位制(有位值十進制)</span></span></dt></dl> <ul><li>中国古代的十進制有书写式和<a href="/wiki/%E7%AE%97%E7%AD%B9" title="算筹">算筹</a>两种型式。</li> <li>印度-阿拉伯十进位制。</li></ul> <div class="mw-heading mw-heading2"><h2 id="方法"><span id=".E6.96.B9.E6.B3.95"></span>方法</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=3" title="编辑章节:方法"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="用文字表示十進整數位"><span id=".E7.94.A8.E6.96.87.E5.AD.97.E8.A1.A8.E7.A4.BA.E5.8D.81.E9.80.B2.E6.95.B4.E6.95.B8.E4.BD.8D"></span>用文字表示十進整數位</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=4" title="编辑章节:用文字表示十進整數位"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>十进位制可以表示任何整數。利用小數點,還可以表示一些小數。 </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84833064"><div role="note" class="hatnote navigation-not-searchable">主条目:<a href="/wiki/%E4%B8%AD%E6%96%87%E6%95%B8%E5%AD%97" class="mw-redirect" title="中文數字">中文數字</a></div> <table class="wikitable" style="border-collapse: collapse; text-align: center;"> <caption><b>十進制漢字列表</b> <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 {\begin{smallmatrix}(10^{n},\;n\geq 0)\end{smallmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mo stretchy="false">(</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>,</mo> <mspace width="thickmathspace" /> <mi>n</mi> <mo>&#x2265;<!-- ≥ --></mo> <mn>0</mn> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{smallmatrix}(10^{n},\;n\geq 0)\end{smallmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8292f6f0c113ed09bf1b1a60295295ad3b3b240" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.829ex; height:2.176ex;" alt="{\displaystyle {\begin{smallmatrix}(10^{n},\;n\geq 0)\end{smallmatrix}}}"></span> </caption> <tbody><tr style="font-family: serif;"> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th><a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6%E8%A9%9E%E9%A0%AD" class="mw-redirect" title="國際單位制詞頭">前綴</a></th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th>前綴</th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th>前綴</th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th><i>n</i></th> <th>10<sup><i>n</i></sup> </th></tr> <tr> <td><b>0</b></td> <td><a href="/wiki/%E4%B8%80" class="mw-redirect" title="一">個</a></td> <td>-</td> <td><b>12</b></td> <td><a href="/wiki/%E5%85%86#1012" title="兆">兆</a>/萬億</td> <td><a href="/wiki/%E5%A4%AA%E6%8B%89" title="太拉">太</a><sup id="cite_ref-hkl214_2-0" class="reference"><a href="#cite_note-hkl214-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup></td> <td><b>24</b></td> <td><a href="/wiki/%E7%A7%AD" title="秭">秭</a></td> <td><a href="/wiki/%E5%B0%A7%E5%AE%83" class="mw-redirect" title="尧它">堯</a></td> <td><b>36</b></td> <td><a href="/w/index.php?title=%E6%BE%97&amp;action=edit&amp;redlink=1" class="new" title="澗(页面不存在)">澗</a></td> <td><b>48</b></td> <td><a href="/w/index.php?title=%E6%A5%B5&amp;action=edit&amp;redlink=1" class="new" title="極(页面不存在)">極</a></td> <td><b>60</b></td> <td><a href="/wiki/%E9%82%A3%E7%94%B1%E4%BB%96" title="那由他">那由他</a></td> <td><b>72</b></td> <td><a href="/wiki/%E7%84%A1%E9%87%8F%E5%A4%A7%E6%95%B8" title="無量大數">大數</a></td> <td><b>84</b></td> <td> </td></tr> <tr> <td><b>1</b></td> <td><a href="/wiki/%E5%8D%81" class="mw-redirect" title="十">十</a></td> <td>-</td> <td><b>13</b></td> <td>十兆</td> <td>-</td> <td><b>25</b></td> <td>十秭</td> <td>-</td> <td><b>37</b></td> <td>十澗</td> <td><b>49</b></td> <td>十極</td> <td><b>61</b></td> <td>十那由他</td> <td><b>73</b></td> <td>十大數</td> <td><b>85</b></td> <td> </td></tr> <tr> <td><b>2</b></td> <td><a href="/wiki/%E7%99%BE" class="mw-redirect" title="百">百</a></td> <td>-</td> <td><b>14</b></td> <td>百兆</td> <td>-</td> <td><b>26</b></td> <td>百秭</td> <td>-</td> <td><b>38</b></td> <td>百澗</td> <td><b>50</b></td> <td>百極</td> <td><b>62</b></td> <td>百那由他</td> <td><b>74</b></td> <td>百大數</td> <td><b>86</b></td> <td> </td></tr> <tr> <td><b>3</b></td> <td><a href="/wiki/%E5%8D%83" class="mw-redirect" title="千">千</a></td> <td><a href="/wiki/%E5%8D%83_(%E5%89%8D%E7%B6%B4)" title="千 (前綴)">千</a></td> <td><b>15</b></td> <td>千兆</td> <td><a href="/wiki/%E6%8B%8D%E5%AE%83" title="拍它">拍</a></td> <td><b>27</b></td> <td>千秭</td> <td><a href="/wiki/%E5%AE%B9%E9%82%A3" title="容那">容</a></td> <td><b>39</b></td> <td>千澗</td> <td><b>51</b></td> <td>千極</td> <td><b>63</b></td> <td>千那由他</td> <td><b>75</b></td> <td>千大數</td> <td><b>87</b></td> <td> </td></tr> <tr> <td><b>4</b></td> <td><a href="/wiki/%E8%90%AC" title="萬">萬</a></td> <td>-</td> <td><b>16</b></td> <td><a href="/wiki/%E4%BA%AC_(%E6%95%B8%E5%AD%97%E5%96%AE%E4%BD%8D)" title="京 (數字單位)">京</a></td> <td>-</td> <td><b>28</b></td> <td><a href="/wiki/%E7%A9%B0" title="穰">穰</a></td> <td>-</td> <td><b>40</b></td> <td><a href="/wiki/%E6%AD%A3#字義以外的使用" title="正">正</a></td> <td><b>52</b></td> <td><a href="/wiki/%E6%81%86%E6%B2%B3%E6%B2%99" title="恆河沙">恒河沙</a></td> <td><b>64</b></td> <td><a href="/wiki/%E4%B8%8D%E5%8F%AF%E6%80%9D%E8%AD%B0" title="不可思議">不可思議</a></td> <td><b>76</b></td> <td></td> <td><b>88</b></td> <td> </td></tr> <tr> <td><b>5</b></td> <td>十萬</td> <td>-</td> <td><b>17</b></td> <td>十京</td> <td>-</td> <td><b>29</b></td> <td>十穰</td> <td>-</td> <td><b>41</b></td> <td>十正</td> <td><b>53</b></td> <td>十恒河沙</td> <td><b>65</b></td> <td>十不可思議</td> <td><b>77</b></td> <td></td> <td colspan="2">…… </td></tr> <tr> <td><b>6</b></td> <td>百萬</td> <td><a href="/wiki/%E7%99%BE%E8%90%AC_(%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6%E6%8E%A5%E9%A0%AD%E8%A9%9E)" class="mw-redirect" title="百萬 (國際單位制接頭詞)">兆</a><sup id="cite_ref-hkl214_2-1" class="reference"><a href="#cite_note-hkl214-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup></td> <td><b>18</b></td> <td>百京</td> <td><a href="/wiki/%E8%89%BE%E5%8F%AF%E8%90%A8" title="艾可萨">艾</a></td> <td><b>30</b></td> <td>百穰</td> <td><a href="/wiki/%E6%98%86%E5%AE%83" title="昆它">昆</a></td> <td><b>42</b></td> <td>百正</td> <td><b>54</b></td> <td>百恒河沙</td> <td><b>66</b></td> <td>百不可思議</td> <td><b>78</b></td> <td></td> <td rowspan="2"><b>100</b></td> <td rowspan="2"><a href="/wiki/%E5%8F%A4%E6%88%88%E7%88%BE" title="古戈爾">古戈爾</a> </td></tr> <tr> <td><b>7</b></td> <td>千萬</td> <td>-</td> <td><b>19</b></td> <td>千京</td> <td>-</td> <td><b>31</b></td> <td>千穰</td> <td>-</td> <td><b>43</b></td> <td>千正</td> <td><b>55</b></td> <td>千恒河沙</td> <td><b>67</b></td> <td>千不可思議</td> <td><b>79</b></td> <td> </td></tr> <tr> <td><b>8</b></td> <td><a href="/wiki/%E5%84%84" title="億">億</a></td> <td>-</td> <td><b>20</b></td> <td><a href="/wiki/%E5%9E%93" title="垓">垓</a></td> <td>-</td> <td><b>32</b></td> <td><a href="/w/index.php?title=%E6%BA%9D&amp;action=edit&amp;redlink=1" class="new" title="溝(页面不存在)">溝</a></td> <td>-</td> <td><b>44</b></td> <td><a href="/wiki/%E8%BC%89" class="mw-disambig" title="載">載</a></td> <td><b>56</b></td> <td><a href="/wiki/%E9%98%BF%E5%83%A7%E7%A5%87" title="阿僧祇">阿僧祇</a></td> <td><b>68</b></td> <td><a href="/wiki/%E7%84%A1%E9%87%8F%E5%A4%A7%E6%95%B8" title="無量大數">無量</a></td> <td><b>80</b></td> <td></td> <td colspan="2">…… </td></tr> <tr> <td><b>9</b></td> <td>十億</td> <td><a href="/wiki/%E5%90%89%E5%92%96" title="吉咖">吉</a></td> <td><b>21</b></td> <td>十垓</td> <td><a href="/wiki/%E6%B3%BD%E5%AE%83" title="泽它">澤</a></td> <td><b>33</b></td> <td>十溝</td> <td>-</td> <td><b>45</b></td> <td>十載</td> <td><b>57</b></td> <td>十阿僧祇</td> <td><b>69</b></td> <td>十無量</td> <td><b>81</b></td> <td></td> <td rowspan="2"><b>10</b><sup>100</sup></td> <td rowspan="2"><a href="/wiki/%E5%8F%A4%E6%88%88%E7%88%BE%E6%99%AE%E5%8B%92%E5%85%8B%E6%96%AF" title="古戈爾普勒克斯">古戈爾普勒克斯</a> </td></tr> <tr> <td><b>10</b></td> <td>百億</td> <td>-</td> <td><b>22</b></td> <td>百垓</td> <td>-</td> <td><b>34</b></td> <td>百溝</td> <td>-</td> <td><b>46</b></td> <td>百載</td> <td><b>58</b></td> <td>百阿僧祇</td> <td><b>70</b></td> <td>百無量</td> <td><b>82</b></td> <td> </td></tr> <tr> <td><b>11</b></td> <td>千億</td> <td>-</td> <td><b>23</b></td> <td>千垓</td> <td>-</td> <td><b>35</b></td> <td>千溝</td> <td>-</td> <td><b>47</b></td> <td>千載</td> <td><b>59</b></td> <td>千阿僧祇</td> <td><b>71</b></td> <td>千無量</td> <td><b>83</b></td> <td></td> <td colspan="2">...... </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="用文字表示十進小數位"><span id=".E7.94.A8.E6.96.87.E5.AD.97.E8.A1.A8.E7.A4.BA.E5.8D.81.E9.80.B2.E5.B0.8F.E6.95.B8.E4.BD.8D"></span>用文字表示十進小數位</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=5" title="编辑章节:用文字表示十進小數位"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84833064"><div role="note" class="hatnote navigation-not-searchable">主条目:<a href="/wiki/%E4%B8%AD%E6%96%87%E6%95%B8%E5%AD%97" class="mw-redirect" title="中文數字">中文數字</a></div> <table class="wikitable" style="border-collapse: collapse; text-align: center;"> <caption><b>十進制漢字列表</b> <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 {\begin{smallmatrix}(10^{n},\;n\leq 0)\end{smallmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle scriptlevel="1"> <mtable rowspacing=".2em" columnspacing="0.333em" displaystyle="false"> <mtr> <mtd> <mo stretchy="false">(</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>,</mo> <mspace width="thickmathspace" /> <mi>n</mi> <mo>&#x2264;<!-- ≤ --></mo> <mn>0</mn> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{smallmatrix}(10^{n},\;n\leq 0)\end{smallmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c21226b689623c0823fd028819592b28c354817" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.829ex; height:2.176ex;" alt="{\displaystyle {\begin{smallmatrix}(10^{n},\;n\leq 0)\end{smallmatrix}}}"></span> </caption> <tbody><tr style="font-family: serif;"> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th>前綴</th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th>前綴</th> <th><i>n</i></th> <th>10<sup><i>n</i></sup></th> <th>前綴 </th></tr> <tr> <td><b>0</b></td> <td><a href="/wiki/%E4%B8%80" class="mw-redirect" title="一">個</a></td> <td>-</td> <td style="white-space: nowrap;"><b>-12</b></td> <td><a href="/w/index.php?title=%E6%BC%A0&amp;action=edit&amp;redlink=1" class="new" title="漠(页面不存在)">漠</a></td> <td><a href="/wiki/%E7%9A%AE%E5%8F%AF" title="皮可">皮</a></td> <td style="white-space: nowrap;"><b>-24</b></td> <td><a href="/wiki/%E6%B6%85%E6%A7%83%E5%AF%82%E9%9D%9C" title="涅槃寂靜">涅槃寂靜</a></td> <td><a href="/wiki/%E6%94%B8" title="攸">幺</a> </td></tr> <tr> <td><b>-1</b></td> <td>分</td> <td>分</td> <td><b>-13</b></td> <td><a href="/wiki/%E5%90%AB%E7%B3%8A" title="含糊">模糊</a></td> <td>-</td> <td><b>-25</b></td> <td></td> <td> </td></tr> <tr> <td><b>-2</b></td> <td><a href="/wiki/%E5%8E%98" title="厘">厘</a></td> <td><a href="/wiki/%E5%8E%98" title="厘">厘</a></td> <td><b>-14</b></td> <td><a href="/w/index.php?title=%E9%80%A1%E5%B7%A1&amp;action=edit&amp;redlink=1" class="new" title="逡巡(页面不存在)">逡巡</a></td> <td>-</td> <td><b>-26</b></td> <td></td> <td> </td></tr> <tr> <td><b>-3</b></td> <td><a href="/wiki/%E6%AF%AB" title="毫">毫</a></td> <td><a href="/wiki/%E6%AF%AB" title="毫">毫</a></td> <td><b>-15</b></td> <td><a href="/wiki/%E9%A0%88%E8%87%BE" title="須臾">須臾</a></td> <td><a href="/wiki/%E9%A3%9E%E6%AF%8D%E6%89%98" title="飞母托">飛</a></td> <td><b>-27</b></td> <td></td> <td><a href="/wiki/%E6%9F%94%E6%89%98" title="柔托">柔</a> </td></tr> <tr> <td><b>-4</b></td> <td><a href="/w/index.php?title=%E7%B5%B2_(%E6%95%B8%E5%90%8D)&amp;action=edit&amp;redlink=1" class="new" title="絲 (數名)(页面不存在)">絲</a></td> <td>-</td> <td><b>-16</b></td> <td><a href="/w/index.php?title=%E7%9E%AC%E6%81%AF&amp;action=edit&amp;redlink=1" class="new" title="瞬息(页面不存在)">瞬息</a></td> <td>-</td> <td><b>-28</b></td> <td></td> <td> </td></tr> <tr> <td><b>-5</b></td> <td><a href="/w/index.php?title=%E5%BF%BD&amp;action=edit&amp;redlink=1" class="new" title="忽(页面不存在)">忽</a></td> <td>-</td> <td><b>-17</b></td> <td><a href="/wiki/%E5%BD%88%E6%8C%87" title="彈指">彈指</a></td> <td>-</td> <td><b>-29</b></td> <td></td> <td> </td></tr> <tr> <td><b>-6</b></td> <td><a href="/wiki/%E5%BE%AE" title="微">微</a></td> <td><a href="/wiki/%E5%BE%AE" title="微">微</a></td> <td><b>-18</b></td> <td><a href="/wiki/%E5%89%8E%E9%82%A3" class="mw-redirect" title="剎那">剎那</a></td> <td><a href="/wiki/%E9%98%BF%E6%89%98" title="阿托">阿</a></td> <td><b>-30</b></td> <td></td> <td><a href="/wiki/%E4%BA%8F%E7%A7%91%E6%89%98" title="亏科托">亏</a> </td></tr> <tr> <td><b>-7</b></td> <td><a href="/w/index.php?title=%E7%BA%96&amp;action=edit&amp;redlink=1" class="new" title="纖(页面不存在)">纖</a></td> <td>-</td> <td><b>-19</b></td> <td><a href="/wiki/%E5%85%AD%E5%BE%B7" class="mw-redirect" title="六德">六德</a></td> <td>-</td> <td><b>-31</b></td> <td></td> <td> </td></tr> <tr> <td><b>-8</b></td> <td><a href="/w/index.php?title=%E6%B2%99_(%E6%95%B8%E5%90%8D)&amp;action=edit&amp;redlink=1" class="new" title="沙 (數名)(页面不存在)">沙</a></td> <td>-</td> <td><b>-20</b></td> <td><a href="/wiki/%E8%99%9B%E7%A9%BA_(%E4%BD%9B%E6%95%99)" title="虛空 (佛教)">虛空</a></td> <td>-</td> <td><b>-32</b></td> <td></td> <td> </td></tr> <tr> <td><b>-9</b></td> <td><a href="/w/index.php?title=%E5%A1%B5_(%E6%95%B8%E5%90%8D)&amp;action=edit&amp;redlink=1" class="new" title="塵 (數名)(页面不存在)">塵</a></td> <td><a href="/wiki/%E5%A5%88" title="奈">奈</a>/<a href="/wiki/%E7%B4%8D" class="mw-redirect" title="納">納</a><sup id="cite_ref-hkl214_2-2" class="reference"><a href="#cite_note-hkl214-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup></td> <td><b>-21</b></td> <td><a href="/wiki/%E6%B8%85%E9%9D%99" title="清静">清靜</a></td> <td><a href="/wiki/%E4%BB%84%E6%99%AE%E6%89%98" title="仄普托">仄</a></td> <td><b>-33</b></td> <td></td> <td> </td></tr> <tr> <td style="white-space: nowrap;"><b>-10</b></td> <td><a href="/wiki/%E5%9F%83%E6%A0%BC%E6%96%AF%E7%89%B9%E6%9C%97" class="mw-redirect" title="埃格斯特朗">埃</a></td> <td>-</td> <td><b>-22</b></td> <td><a href="/w/index.php?title=%E9%98%BF%E8%B3%B4%E8%80%B6&amp;action=edit&amp;redlink=1" class="new" title="阿賴耶(页面不存在)">阿賴耶</a></td> <td>-</td> <td><b>-34</b></td> <td></td> <td> </td></tr> <tr> <td><b>-11</b></td> <td><a href="/wiki/%E6%B8%BA" class="mw-redirect" title="渺">渺</a></td> <td>-</td> <td><b>-23</b></td> <td><a href="/w/index.php?title=%E9%98%BF%E6%91%A9%E7%BE%85&amp;action=edit&amp;redlink=1" class="new" title="阿摩羅(页面不存在)">阿摩羅</a></td> <td>-</td> <td><b>-35</b></td> <td></td> <td> </td></tr></tbody></table> <p>註: </p> <ul><li><b>厘</b>亦作<b>釐</b>。</li> <li><b>毫</b>亦作<b>毛</b>。</li> <li><b>漠</b>是正寫,而<b>莫</b>並非正確寫法。</li> <li>比<b>漠</b>微細的,是自<a href="/wiki/%E5%A4%A9%E7%AB%BA" title="天竺">天竺</a>佛經上的數字。而這些「佛經數字」已成為古代用法了。</li></ul> <div class="mw-heading mw-heading2"><h2 id="历史沿革"><span id=".E5.8E.86.E5.8F.B2.E6.B2.BF.E9.9D.A9"></span>历史沿革</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=6" title="编辑章节:历史沿革"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Oracle_numeral.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Oracle_numeral.jpg/330px-Oracle_numeral.jpg" decoding="async" width="330" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Oracle_numeral.jpg/495px-Oracle_numeral.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Oracle_numeral.jpg/660px-Oracle_numeral.jpg 2x" data-file-width="1213" data-file-height="403" /></a><figcaption>甲骨文十进数字</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Qinghuajian,_Suan_Biao.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Qinghuajian%2C_Suan_Biao.jpg/300px-Qinghuajian%2C_Suan_Biao.jpg" decoding="async" width="300" height="412" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Qinghuajian%2C_Suan_Biao.jpg/450px-Qinghuajian%2C_Suan_Biao.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Qinghuajian%2C_Suan_Biao.jpg/600px-Qinghuajian%2C_Suan_Biao.jpg 2x" data-file-width="1528" data-file-height="2096" /></a><figcaption>世界上最早的十進制乘法表文物:清华简《算表》</figcaption></figure> <p>中文自始至终都是使用十進制,没有任何使用其他進制的证据。 </p><p>有学者认为,<a href="/wiki/%E5%8C%97%E4%BA%AC" class="mw-redirect" title="北京">北京</a><a href="/wiki/%E5%91%A8%E5%8F%A3%E5%BA%97" class="mw-redirect" title="周口店">周口店</a>的一万多年前的<a href="/wiki/%E5%B1%B1%E9%A1%B6%E6%B4%9E%E4%BA%BA" title="山顶洞人">山顶洞人</a>遗址出土的<a href="/w/index.php?title=%E9%AA%A8%E7%AE%A1&amp;action=edit&amp;redlink=1" class="new" title="骨管(页面不存在)">骨管</a>,以一个圆点代表1,两个圆点并列代表2,三个圆点并列代表3,五个圆点上二下三排列代表5,长圆形可能代表十。中国著名数学史家,国际科学史研究院通讯院士<a href="/wiki/%E6%9D%8E%E8%BF%AA" class="mw-disambig" title="李迪">李迪</a>教授认为山顶洞人骨管符号是“一种十進制思想”<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup>。 </p><p>另有学者对中国<a href="/wiki/%E9%9D%92%E6%B5%B7" class="mw-redirect" title="青海">青海</a><a href="/wiki/%E4%B9%90%E9%83%BD%E5%8E%BF" class="mw-redirect" title="乐都县">乐都县</a>柳湾出土一千多枚<a href="/wiki/%E6%96%B0%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3" title="新石器时代">新石器时代</a>骨片进行研究,发现它们分属马厂、半山、齐家和辛店四个中文化型。骨片长度为2-2.4厘米,厚约1毫米。骨片上有刻痕,少的一个,多不超过八个,每个骨片上的刻痕数目不超过十个,他们以此认为新石器时代已有加法运算和十進制<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup>。 </p><p>另有学者认为,<a href="/wiki/%E7%94%B2%E9%AA%A8%E6%96%87" title="甲骨文">甲骨文</a>中一横代表1,两横相叠代表二,三横代表三,四横代表四,X 代表五,“人”形代表六,“十”代表七,“)(”代表八, “九”已经是九;| 代表十,||代表20,|||代表三十,||||代表四十;此外50,60,70,80,90,100,200,300,400,500,600,700,800,900,1000,2000,……9000,10000……40000 都有不同的符号。商代甲骨文“已形成完整的十進制系统”。<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup> </p><p>北京的<a href="/wiki/%E4%B8%AD%E5%9B%BD%E5%8E%86%E5%8F%B2%E5%8D%9A%E7%89%A9%E9%A6%86" class="mw-redirect" title="中国历史博物馆">中国历史博物馆</a>藏有一把<a href="/wiki/%E5%AE%89%E9%98%B3" class="mw-redirect" title="安阳">安阳</a><a href="/wiki/%E6%AE%B7%E5%A2%9F" title="殷墟">殷墟</a>出土的象牙尺,长15.78厘米,分为十寸,说明中国商代的十進制几经用在长度上了。 </p><p>中国<a href="/wiki/%E5%91%A8%E4%BB%A3" class="mw-redirect" title="周代">周代</a><a href="/wiki/%E9%87%91%E6%96%87" title="金文">金文</a>的纪数法,继承商代的十進制, 又有明显的进步,十进数量级符号有十、百、千、万、亿,如西周金文“伐鬼方……俘万三千八十一人”,“武王遂征四方,俘人三亿万有二百三十”,出现了位值记数,例如 “俘牛三百五十五“,其中三百五十五写成“三全XX”,前面的“全”是金文的“百”,后面两个XX是五十五,省去了“十”,出现了位置概念,但尚未形成完整的位值概念。金文<a href="/w/index.php?title=%E5%95%86%E9%9E%85%E9%87%8F%E9%93%AD&amp;action=edit&amp;redlink=1" class="new" title="商鞅量铭(页面不存在)">商鞅量铭</a>还出现分数。<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">&#91;</span>6<span class="cite-bracket">&#93;</span></a></sup> </p><p>春秋战国时代,出现严格的十进位制<a href="/wiki/%E7%AD%B9%E7%AE%97" title="筹算">筹算</a>记数,以空代表0,也发明了用于十进位制乘法、除法的<a href="/wiki/%E4%B9%9D%E4%B9%9D%E8%A1%A8" title="九九表">九九表</a>和《<a href="/wiki/%E7%AE%97%E8%A1%A8" class="mw-redirect" title="算表">算表</a>》。 </p><p>公元前3400年左右,<a href="/wiki/%E5%8F%A4%E5%9F%83%E5%8F%8A" title="古埃及">古埃及</a>有基于十進制的记数法。<sup id="cite_ref-数学史概论,13页_7-0" class="reference"><a href="#cite_note-数学史概论,13页-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup>但这种十進制并无位值的概念。<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">&#91;</span>8<span class="cite-bracket">&#93;</span></a></sup> </p><p><a href="/wiki/%E5%90%A0%E9%99%80%E6%97%B6%E4%BB%A3" class="mw-redirect" title="吠陀时代">吠陀时代</a>前800年的印度<a href="/wiki/%E4%BB%AA%E8%BD%A8%E7%BB%8F" title="仪轨经">仪轨经</a>类文献中的<a href="/wiki/%E7%BB%B3%E6%B3%95%E7%BB%8F" class="mw-redirect" title="绳法经">绳法经</a>中包含大量分数的应用,但并无证据显示此时的文字记数系统是十進制的。<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup> </p><p>公元前500年,<a href="/wiki/%E5%B8%8C%E8%85%8A" title="希腊">希腊</a><a href="/wiki/%E5%8F%A4%E5%85%B8%E6%97%B6%E6%9C%9F" class="mw-redirect" title="古典时期">古典时期</a>的<a href="/wiki/%E9%98%BF%E6%8F%90%E5%8D%A1" title="阿提卡">阿提卡</a>数字为十進制系统。<sup id="cite_ref-数学史概论,13页_7-1" class="reference"><a href="#cite_note-数学史概论,13页-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup> </p><p>公元前300年,印度的<a href="/w/index.php?title=%E5%A9%86%E7%BD%97%E8%BF%B7&amp;action=edit&amp;redlink=1" class="new" title="婆罗迷(页面不存在)">婆罗迷</a>数字为十進制。<sup id="cite_ref-数学史概论,13页_7-2" class="reference"><a href="#cite_note-数学史概论,13页-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup><a href="/w/index.php?title=%E5%A9%86%E7%BD%97%E8%BF%B7%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="婆罗迷十进制(页面不存在)">婆罗迷十进制</a>毫无位值概念。 </p><p>出土于<a href="/wiki/%E5%B7%B4%E5%9F%BA%E6%96%AF%E5%9D%A6" title="巴基斯坦">巴基斯坦</a>的古印度<a href="/w/index.php?title=%E5%B7%B4%E5%85%8B%E6%B2%99%E5%88%A9%E6%89%8B%E7%A8%BF&amp;action=edit&amp;redlink=1" class="new" title="巴克沙利手稿(页面不存在)">巴克沙利手稿</a>可能是世界上最早的包括<a href="/wiki/0" title="0">0</a>的“真正的”十進制系统,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">&#91;</span>10<span class="cite-bracket">&#93;</span></a></sup>但它的具体时间有争议。<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="起源"><span id=".E8.B5.B7.E6.BA.90"></span>起源</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=7" title="编辑章节:起源"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Rod_calculus_addition.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Rod_calculus_addition.GIF/100px-Rod_calculus_addition.GIF" decoding="async" width="100" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Rod_calculus_addition.GIF/150px-Rod_calculus_addition.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Rod_calculus_addition.GIF/200px-Rod_calculus_addition.GIF 2x" data-file-width="593" data-file-height="424" /></a><figcaption>筹算加法</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:LABBANADD.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/LABBANADD.GIF/100px-LABBANADD.GIF" decoding="async" width="100" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/LABBANADD.GIF/150px-LABBANADD.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/LABBANADD.GIF/200px-LABBANADD.GIF 2x" data-file-width="528" data-file-height="450" /></a><figcaption>伊本·拉班加法</figcaption></figure> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Sunzi_division.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Sunzi_division.GIF/110px-Sunzi_division.GIF" decoding="async" width="110" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Sunzi_division.GIF/165px-Sunzi_division.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Sunzi_division.GIF/220px-Sunzi_division.GIF 2x" data-file-width="443" data-file-height="364" /></a><figcaption>公元400年的孙子除法 6561/9</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:AL_Khwarizmi_division.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/AL_Khwarizmi_division.GIF/110px-AL_Khwarizmi_division.GIF" decoding="async" width="110" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/AL_Khwarizmi_division.GIF/165px-AL_Khwarizmi_division.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/AL_Khwarizmi_division.GIF/220px-AL_Khwarizmi_division.GIF 2x" data-file-width="443" data-file-height="364" /></a><figcaption>公元825年花拉子米除法,和孙子除法雷同</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Kushyar_ibn_Labban_division.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Kushyar_ibn_Labban_division.GIF/110px-Kushyar_ibn_Labban_division.GIF" decoding="async" width="110" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Kushyar_ibn_Labban_division.GIF/165px-Kushyar_ibn_Labban_division.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Kushyar_ibn_Labban_division.GIF/220px-Kushyar_ibn_Labban_division.GIF 2x" data-file-width="356" data-file-height="339" /></a><figcaption>10世纪波斯数学家<a href="/w/index.php?title=%E4%BC%8A%E6%9C%AC%C2%B7_%E6%8B%89%E7%8F%AD&amp;action=edit&amp;redlink=1" class="new" title="伊本· 拉班(页面不存在)">伊本· 拉班</a>的除法,也源自孙子除法</figcaption></figure> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Sunzi_sqrt.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sunzi_sqrt.GIF/120px-Sunzi_sqrt.GIF" decoding="async" width="120" height="114" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sunzi_sqrt.GIF/180px-Sunzi_sqrt.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sunzi_sqrt.GIF/240px-Sunzi_sqrt.GIF 2x" data-file-width="657" data-file-height="622" /></a><figcaption>筹算开方术</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Labbansqrt.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Labbansqrt.GIF/120px-Labbansqrt.GIF" decoding="async" width="120" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Labbansqrt.GIF/180px-Labbansqrt.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Labbansqrt.GIF/240px-Labbansqrt.GIF 2x" data-file-width="528" data-file-height="450" /></a><figcaption>伊本拉班开方与筹算开方类同</figcaption></figure> <p>一般“共识”认为现在世界通行的十進制起源于印度。从20世纪初,国际上许多学者,包括<a href="/wiki/%E6%9D%8E%E7%BA%A6%E7%91%9F" title="李约瑟">李约瑟</a>在内对印度起源论提出了质疑。 </p> <ul><li>早在1907年印度学者Kaye指出“我研究的目的,在于指出我们关于现代数学记数的基础很不牢固,值得重新研究。从印度文字,碑文证据,早期印度日的记数法,以及现代印度土著的风俗习惯等方面,指明现代记数可能来自外国<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">&#91;</span>12<span class="cite-bracket">&#93;</span></a></sup></li> <li>印度学者Datta and Singh认为,“印度不存在记述这些数字及其基本算术运算方法的早期文献,发明人不可知”<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">&#91;</span>13<span class="cite-bracket">&#93;</span></a></sup></li> <li>德国学者Menninger 认为印度十進制的起源,模糊不清。<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">&#91;</span>14<span class="cite-bracket">&#93;</span></a></sup></li> <li><a href="/wiki/%E6%9D%8E%E7%BA%A6%E7%91%9F" title="李约瑟">李约瑟</a>指出,古印度的数字系统,用单独的符号表示10和10的倍数,相对于<a href="/wiki/%E5%B8%8C%E8%85%8A" title="希腊">希腊</a>或<a href="/wiki/%E5%B8%8C%E4%BC%AF%E4%BE%86" class="mw-redirect" title="希伯來">希伯来</a>数字系统,毫无进步……印度数字中的0,很可能起源于东印度和中国南方文化接壤的地区。印度是否采纳中国算筹的空档而受启发?关键在于中国在比<a href="/wiki/%E5%AD%99%E5%AD%90%E7%AE%97%E7%BB%8F" title="孙子算经">孙子算经</a>早很多的时期,已经拥有十进位制。<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">&#91;</span>15<span class="cite-bracket">&#93;</span></a></sup></li> <li>曾任小学教师的法国通俗作家Ifrah断言,458年的<a href="/wiki/%E5%8D%B0%E5%BA%A6" title="印度">印度</a><a href="/wiki/%E8%80%86%E9%82%A3%E6%95%99" title="耆那教">耆那教</a>文献<i>Lokavibhaga</i>中的 <i>panchabhyah khalu shunyebhyah param dve sapta chambaram ekam trini cha rupam cha</i>代表“五空和二和七和天,一和三和形,就是13107200000”,“是世界上最早的带零的十進制数字”。<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">&#91;</span>16<span class="cite-bracket">&#93;</span></a></sup>。他还说,印度的零、一、二、……九的词多了,有eka,pitamaha,adi,tanu……都指“一”,dvi,ashvin,Yama, yamala, netra,bahu,guophau, paksha 都可以是“二”……<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">&#91;</span>17<span class="cite-bracket">&#93;</span></a></sup>。有学者认为现在世界各国使用的<a href="/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B0%E5%AD%97" title="阿拉伯数字">阿拉伯数字</a>都起源于这一系统。<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">&#91;</span>18<span class="cite-bracket">&#93;</span></a></sup></li> <li>美国学者Robert Temple根据<a href="/wiki/%E6%9D%8E%E7%BA%A6%E7%91%9F" title="李约瑟">李约瑟</a>《中国科学技术史》缩写的“Genius of China”,认为今日世界通行的十進制,真正起源地在中国<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">&#91;</span>19<span class="cite-bracket">&#93;</span></a></sup>。</li> <li>新加坡著名数学史家<a href="/wiki/%E5%85%B0%E4%B8%BD%E8%93%89" class="mw-redirect" title="兰丽蓉">兰丽蓉</a>认为<a href="/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B0%E5%AD%97" title="阿拉伯数字">阿拉伯数字</a>的基本概念,不可能起源于印度<a href="/w/index.php?title=%E5%A9%86%E7%BD%97%E8%BF%B7&amp;action=edit&amp;redlink=1" class="new" title="婆罗迷(页面不存在)">婆罗迷</a>数字,而是起源于中国<a href="/wiki/%E7%AD%B9%E7%AE%97" title="筹算">筹算</a>。筹算用九个符号代表一切数,其加法减法,天然包含在算筹之中,三减三就是从算版上取去三个算筹,算版上自然而然留下一个空位,这就是零,筹算中称为‘空’。无独有偶,印度在没有发明‘0’这个符号之前,和中国的<a href="/wiki/%E7%AD%B9%E7%AE%97" title="筹算">筹算</a>一摸一样,也用一格空档来表示零,称为“sunya”!,这就没有天然的理由了;而“983 542”到底是一个数字还是两个数值,容易产生混淆,后来印度才用“.”或“0”代表sunya。此外印度的加减乘除运算程序,上、中、下三行排列的方式,除数和被除数首位对齐,留筹算式的空白(!)而非“0”,从左往右计算的规则,商数右边留空白而没有补“0”,每算一步之后,除数右移一位,甚至余数表示为分数的上、中、下三行表示方法,居然和<a href="/wiki/%E5%AD%99%E5%AD%90%E7%AE%97%E7%BB%8F" title="孙子算经">孙子算经</a>中叙述的孙子除法雷同,这三点是印度十進制数字系统的基础概念全盘来自筹算的铁证。<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">&#91;</span>20<span class="cite-bracket">&#93;</span></a></sup>。</li></ul> <p>现存最古老的运用<a href="/wiki/%E5%8D%B0%E5%BA%A6%E6%95%B8%E5%AD%97" title="印度數字">印度数字</a>的算术著作:10世纪<a href="/wiki/%E6%B3%A2%E6%96%AF" title="波斯">波斯</a>数学家<a href="/wiki/%E4%BC%8A%E6%9C%AC%C2%B7%E6%8B%89%E7%8F%AD" title="伊本·拉班">伊本·拉班</a>在所著《<a href="/wiki/%E5%8D%B0%E5%BA%A6%E7%AE%97%E6%9C%AF%E5%8E%9F%E7%90%86" title="印度算术原理">印度算术原理</a>》中详细叙述的印度除法,印度开平方术,开立方术也同样源自孙子算经<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">&#91;</span>21<span class="cite-bracket">&#93;</span></a></sup> </p><p>0……9符号来自印度,但背后的十进位制概念,则来自筹算。将空写成0,只是书写方式,没有概念上的发明。至于中国筹算十進制如何传入印度,兰丽蓉认为中国古时官员,商人僧侣和旅行家,腰挂算筹袋很平常,而中国和印度来往密切,传入印度不难理解。事实上早于458年一个半世纪,从公元266-399年间,就有竺法护,康法郎,于法蓝,竺佛念,慧常,进行,慧辩,支法领,法净等高僧到过印度了,此后还有著名的<a href="/wiki/%E6%B3%95%E6%98%BE" title="法显">法显</a>到过佛国。 </p> <div class="mw-heading mw-heading3"><h3 id="印度与阿拉伯的十进位制"><span id=".E5.8D.B0.E5.BA.A6.E4.B8.8E.E9.98.BF.E6.8B.89.E4.BC.AF.E7.9A.84.E5.8D.81.E8.BF.9B.E4.BD.8D.E5.88.B6"></span>印度与阿拉伯的十进位制</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=8" title="编辑章节:印度与阿拉伯的十进位制"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>七世纪之前,印度数字用一到九个符号,以空代零。<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">&#91;</span>22<span class="cite-bracket">&#93;</span></a></sup>。时至今日,南印度<a href="/wiki/%E6%B3%B0%E7%B1%B3%E5%B0%94%E7%BA%B3%E5%BE%B7%E9%82%A6" title="泰米尔纳德邦">泰米尔纳德邦</a>仍通行九个符号加空代零,另有十、百、千符号<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">&#91;</span>23<span class="cite-bracket">&#93;</span></a></sup>。</li> <li>公元七世纪,印度Nagari数字出现0。<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">&#91;</span>24<span class="cite-bracket">&#93;</span></a></sup></li> <li>公元八世纪唐朝太史监印度人<a href="/wiki/%E7%9E%BF%E6%9B%87%E6%82%89%E9%81%94" title="瞿曇悉達">瞿昙悉达</a>在<a href="/wiki/%E5%BC%80%E5%85%83" title="开元">开元</a>年间主持编纂的《<a href="/wiki/%E9%96%8B%E5%85%83%E5%8D%A0%E7%B6%93" title="開元占經">开元占经</a>》卷104将印度数字“·”(零)引入中国,“右天竺算法用上件九个字乘除,其字皆一举扎而成,凡数至十进入前位,每空位处恒安一点”,但只有文字叙述,未曾画出印度数吗的形状。<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">&#91;</span>25<span class="cite-bracket">&#93;</span></a></sup></li> <li>学界公认,印度带“0”的十进位制最早出现在876年印度<a href="/wiki/%E7%93%9C%E5%BB%96%E5%B0%94" title="瓜廖尔">瓜廖尔</a>Bhojadera碑文,“933”年印度历(公元876年)碑文文记述一块“270” 乘 “187” 的花园,每日给庙奉献“50”个花圈。<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">&#91;</span>26<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">&#91;</span>27<span class="cite-bracket">&#93;</span></a></sup>“933”、“270”、“187”、“50”四个印度数字,已经是现代阿拉伯数字了。</li> <li>印度本土用<a href="/wiki/%E5%8D%B0%E5%BA%A6%E6%95%B8%E5%AD%97" title="印度數字">印度数字</a>的算术著作已荡然无存,但保留在多种阿拉伯文著作中。存世最古老的一本用<a href="/wiki/%E5%8D%B0%E5%BA%A6%E6%95%B8%E5%AD%97" title="印度數字">印度数字</a>的算术书,当推十世纪<a href="/wiki/%E6%B3%A2%E6%96%AF" title="波斯">波斯</a>数学家<a href="/wiki/%E4%BC%8A%E6%9C%AC%C2%B7%E6%8B%89%E7%8F%AD" title="伊本·拉班">伊本·拉班</a>所著的《<a href="/wiki/%E5%8D%B0%E5%BA%A6%E7%AE%97%E6%9C%AF%E5%8E%9F%E7%90%86" title="印度算术原理">印度算术原理</a>》,他在该书第一章详细叙述印度十进位制数字的原理。他写道“必须认识九个数字۹۸۷۶۵۴۳۲۱,第一个是一,第二个是二,一直到九,并且头一个是个位,第二个是十位,第三百位,第四千位,第五万……十之后必须加一个零,一百之后必须加两个零,即记十为10,百为100。</li> <li>九世纪花拉子米,十世纪伊本·拉班,十一世纪<a href="/w/index.php?title=%E4%B9%8C%E5%85%8B%E9%87%8C%E8%BF%AA%E8%A5%BF&amp;action=edit&amp;redlink=1" class="new" title="乌克里迪西(页面不存在)">乌克里迪西</a>等阿拉伯数学家都著有关于印度算术的著作,所述的加、减、乘、除、开平方、开立方的程序,从排列方式,留空方式,数字位移方式,以至余数、分数的表示格式,都和中国公元一世纪的<a href="/wiki/%E4%B9%9D%E7%AB%A0%E7%AE%97%E6%9C%AF" title="九章算术">九章算术</a>、5世纪<a href="/wiki/%E5%AD%99%E5%AD%90%E7%AE%97%E7%BB%8F" title="孙子算经">孙子算经</a>所述的相应算术运算相同。中世纪的印度-阿拉伯数学家用沙盘进行计算.沙盘可以是带沙子的地面或一块木板,上铺一层薄沙,划上格子,用手指头或一根棍将阿拉伯数字划在格子里面。因为有格子,所以空格就代表零,不必写“0”<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">&#91;</span>28<span class="cite-bracket">&#93;</span></a></sup>,这和中国筹算以空代零的习惯一样<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">&#91;</span>29<span class="cite-bracket">&#93;</span></a></sup>。</li> <li>印度文数字的0,1,2……9中的“0”,是印度数学对十进位制的重要贡献,它克服了算筹数码空档的缺点,例如<span typeof="mw:File"><a href="/wiki/File:Counting_rod_v6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Counting_rod_v6.png/12px-Counting_rod_v6.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Counting_rod_v6.png/18px-Counting_rod_v6.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Counting_rod_v6.png/24px-Counting_rod_v6.png 2x" data-file-width="29" data-file-height="32" /></a></span>可以指6,600,60000……使十进位制草算在中世纪阿拉伯国家大为流行。</li> <li>中国南宋数学家<a href="/wiki/%E7%A7%A6%E4%B9%9D%E9%9F%B6" title="秦九韶">秦九韶</a>在算筹码中引入圆圈<span typeof="mw:File"><a href="/wiki/File:Counting_rod_0.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Counting_rod_0.png/12px-Counting_rod_0.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Counting_rod_0.png/18px-Counting_rod_0.png 1.5x, //upload.wikimedia.org/wikipedia/commons/5/50/Counting_rod_0.png 2x" data-file-width="23" data-file-height="23" /></a></span>可能受到印度“0”的影响。</li></ul> <div class="mw-heading mw-heading2"><h2 id="十进-{制}-與度量衡"><span id=".E5.8D.81.E8.BF.9B-.7B.E5.88.B6.7D-.E8.88.87.E5.BA.A6.E9.87.8F.E8.A1.A1"></span>十进制與度量衡</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=9" title="编辑章节:十进制與度量衡"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>中国十進制度量衡有久远的历史。公元前6世纪的一把周朝尺刻有十分之一的寸和百分之一的分。<sup id="cite_ref-法国马若安著《中算史导论》_第十二章_30-0" class="reference"><a href="#cite_note-法国马若安著《中算史导论》_第十二章-30"><span class="cite-bracket">&#91;</span>30<span class="cite-bracket">&#93;</span></a></sup></li> <li>王莽官定一百副青铜容量标准,一斛=十斗,一斗=十升,一升=十合。<sup id="cite_ref-法国马若安著《中算史导论》_第十二章_30-1" class="reference"><a href="#cite_note-法国马若安著《中算史导论》_第十二章-30"><span class="cite-bracket">&#91;</span>30<span class="cite-bracket">&#93;</span></a></sup></li></ul> <p>傳統<a href="/wiki/%E5%BA%A6%E9%87%8F%E8%A1%A1" class="mw-disambig" title="度量衡">度量衡</a>不是完全使用十进制,例如1<a href="/wiki/%E6%96%A4" title="斤">斤</a>等於16<a href="/wiki/%E5%85%A9" class="mw-redirect" title="兩">兩</a>、1<a href="/wiki/%E5%91%8E" class="mw-redirect" title="呎">呎</a>等於12<a href="/wiki/%E5%90%8B" class="mw-redirect" title="吋">吋</a>等。<a href="/wiki/%E5%85%AC%E5%88%B6" title="公制">公制</a>完全使用十进制,使換算較直接。<a href="/wiki/%E4%B8%AD%E8%8F%AF%E6%B0%91%E5%9C%8B%E6%94%BF%E5%BA%9C" title="中華民國政府">中華民國政府</a>於1920年代推行<a href="/wiki/%E5%B8%82%E5%88%B6" title="市制">市制</a>以與公制接軌。1980年代<a href="/wiki/%E9%A6%99%E6%B8%AF%E6%94%BF%E5%BA%9C" class="mw-redirect" title="香港政府">香港政府</a>便曾大力宣傳十进制的好處,當時有口號如「採用十进制,公道又易計」或「十进制,好易計」等,但民間至今仍常用舊制、英制等非十進制換算。 </p> <div class="mw-heading mw-heading2"><h2 id="清华简算表"><span id=".E6.B8.85.E5.8D.8E.E7.AE.80.E7.AE.97.E8.A1.A8"></span>清华简算表</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=10" title="编辑章节:清华简算表"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84833064"><div role="note" class="hatnote navigation-not-searchable">主条目:<a href="/wiki/%E7%AE%97%E8%A1%A8_(%E6%B8%85%E5%8D%8E%E7%AE%80)" title="算表 (清华简)">算表 (清华简)</a></div> <p>成于公元前300年左右的清华简《<a href="/wiki/%E7%AE%97%E8%A1%A8" class="mw-redirect" title="算表">算表</a>》是世界上最早的十進制乘法表<sup id="cite_ref-nature.com_31-0" class="reference"><a href="#cite_note-nature.com-31"><span class="cite-bracket">&#91;</span>31<span class="cite-bracket">&#93;</span></a></sup>。 </p><p>美国数学史家约瑟夫·道本周(Joseph Dauben)说《算表》是世界上最早的十進制乘法表文物<sup id="cite_ref-nature.com_31-1" class="reference"><a href="#cite_note-nature.com-31"><span class="cite-bracket">&#91;</span>31<span class="cite-bracket">&#93;</span></a></sup>。 </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Qinghuajian_Suan_Biao_example.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Qinghuajian_Suan_Biao_example.svg/600px-Qinghuajian_Suan_Biao_example.svg.png" decoding="async" width="600" height="338" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Qinghuajian_Suan_Biao_example.svg/900px-Qinghuajian_Suan_Biao_example.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Qinghuajian_Suan_Biao_example.svg/1200px-Qinghuajian_Suan_Biao_example.svg.png 2x" data-file-width="512" data-file-height="288" /></a><figcaption>战国时代(公元前300年)《算表》示意图,并用于计算12 × 34.5</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=11" title="编辑章节:参考文献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-count references-column-count-2" style="-moz-column-count: 2; -webkit-column-count: 2; column-count: 2; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">数学史概论,李文林,<a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/7040113619" class="internal mw-magiclink-isbn">ISBN 7-04-011361-9</a>,14页</span> </li> <li id="cite_note-hkl214-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-hkl214_2-0"><sup><b>2.0</b></sup></a> <a href="#cite_ref-hkl214_2-1"><sup><b>2.1</b></sup></a> <a href="#cite_ref-hkl214_2-2"><sup><b>2.2</b></sup></a></span> <span class="reference-text">香港法例第214章《十進制條例》附表1</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"><a href="/wiki/%E5%90%B4%E6%96%87%E4%BF%8A" title="吴文俊">吴文俊</a>院士主编《<a href="/wiki/%E4%B8%AD%E5%9B%BD%E6%95%B0%E5%AD%A6%E5%8F%B2%E5%A4%A7%E7%B3%BB" class="mw-disambig" title="中国数学史大系">中国数学史大系</a>》第一卷 上古到西汉 127页 <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/7303045554" class="internal mw-magiclink-isbn">ISBN 7-303-04555-4</a>/O 引<a href="/wiki/%E6%9D%8E%E8%BF%AA" class="mw-disambig" title="李迪">李迪</a> 《中国数学史简编》 5-6 1984</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="/wiki/%E5%90%B4%E6%96%87%E4%BF%8A" title="吴文俊">吴文俊</a>院士主编《中国数学史大系》第一卷上古到西汉 129页</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="/wiki/%E5%90%B4%E6%96%87%E4%BF%8A" title="吴文俊">吴文俊</a>院士主编《<a href="/wiki/%E4%B8%AD%E5%9B%BD%E6%95%B0%E5%AD%A6%E5%8F%B2%E5%A4%A7%E7%B3%BB" class="mw-disambig" title="中国数学史大系">中国数学史大系</a>》第一卷 上古到西汉 127页 <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/7303045554" class="internal mw-magiclink-isbn">ISBN 7-303-04555-4</a>/O 144-151</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="/wiki/%E5%90%B4%E6%96%87%E4%BF%8A" title="吴文俊">吴文俊</a>院士主编《中国数学史大系》第一卷《上古到西汉》第三章《金文中的数学》 177页</span> </li> <li id="cite_note-数学史概论,13页-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-数学史概论,13页_7-0"><sup><b>7.0</b></sup></a> <a href="#cite_ref-数学史概论,13页_7-1"><sup><b>7.1</b></sup></a> <a href="#cite_ref-数学史概论,13页_7-2"><sup><b>7.2</b></sup></a></span> <span class="reference-text">数学史概论,13页</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">前引书,18页</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">数学史概论,106页</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">数学史概论,107页</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Bibhutibhusan Datta (Volume 35, Number 4 (1929), 579–580.). Review: G. R. Kaye, The Bakhshâlî Manuscript—A Study in Mediaeval Mathematics, 1927. Bull. Amer. Math. Soc.. <a rel="nofollow" class="external free" href="http://projecteuclid.org/euclid.bams/1183493367">http://projecteuclid.org/euclid.bams/1183493367</a> (<a rel="nofollow" class="external text" href="//web.archive.org/web/20151129184338/http://projecteuclid.org/euclid.bams/1183493367">页面存档备份</a>,存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>). Retrieved 2007-07-24.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Kaye, G,R, Notes On Indian Mathematics, Arithmetical notation. Journal of the Asiatic Society of Bengal</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Datta &amp; Singh, History of Hindu mathematics, Bombay,1962</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Menninger:Number Words and number symbols, MIT Press 1969</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a href="/wiki/%E6%9D%8E%E7%BA%A6%E7%91%9F" title="李约瑟">李约瑟</a>原著 柯林·罗南改编 上海交通大学科学史系翻译 《中华科学文明史》 第二卷 第一章 数学</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Ifrah, Georges (2000) The Universal History of Numbers: From Prehistory to the Invention of the Computer, Wiley. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0471393401" class="internal mw-magiclink-isbn">ISBN 0-471-39340-1</a>,416页 “five voids, then two and seven,the sky, one and three and the form"</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">同上410页</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">数学史概论,108页</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">Robert Temple, The Genius of China, with preface by Joseph Needham。 139 <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9781853752926" class="internal mw-magiclink-isbn">ISBN 9781853752926</a>。</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">Lam Lai Yong,A Chinese Genesis, Rewriting the history of our numeral system. Archive for History of Exact Science 38 101-108</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">Lam Lay Yong, Fleeting Footsteps, p44, 图i至v</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">George Ifrah, The Universal History of Numbers, p378-380</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">George Ifrah,p372</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">George Ifrah, p380</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">吴文俊主编 中国数学史大系 卷4 418页</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text">李约瑟原著,柯林·罗南改编中华科学技术史 2,第一章 数学</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">George Ifrah,The Universal History of Numbers, From Prehistory to the Invention of Computers, P400 Wiley <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0965045501" class="internal mw-magiclink-isbn">ISBN 0-9650455-0-1</a></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">George Ifrah, The Universal History of Numbers, p555-556, Wiley</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">The conceptual origins of our numeral system and the symbolic form of algebra. Archive for History of Exact Sciences 36: 183-195. Lam Lay-Yong. 1987</span> </li> <li id="cite_note-法国马若安著《中算史导论》_第十二章-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-法国马若安著《中算史导论》_第十二章_30-0"><sup><b>30.0</b></sup></a> <a href="#cite_ref-法国马若安著《中算史导论》_第十二章_30-1"><sup><b>30.1</b></sup></a></span> <span class="reference-text">法国马若安著《中算史导论》 第十二章</span> </li> <li id="cite_note-nature.com-31"><span class="mw-cite-backlink">^ <a href="#cite_ref-nature.com_31-0"><sup><b>31.0</b></sup></a> <a href="#cite_ref-nature.com_31-1"><sup><b>31.1</b></sup></a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.nature.com/news/ancient-times-table-hidden-in-chinese-bamboo-strips-1.14482">The 2,300-year-old matrix is the world's oldest decimal multiplication table.自然杂志</a>. <span class="reference-accessdate"> &#91;<span class="nowrap">2014-03-12</span>&#93;</span>. (原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190913095052/http://www.nature.com/news/ancient-times-table-hidden-in-chinese-bamboo-strips-1.14482">存档</a>于2019-09-13).</cite><span title="ctx_ver=Z39.88-2004&amp;rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E5%8D%81%E8%BF%9B%E5%88%B6&amp;rft.btitle=The+2%2C300-year-old+matrix+is+the+world%27s+oldest+decimal+multiplication+table.%E8%87%AA%E7%84%B6%E6%9D%82%E5%BF%97&amp;rft.genre=unknown&amp;rft_id=http%3A%2F%2Fwww.nature.com%2Fnews%2Fancient-times-table-hidden-in-chinese-bamboo-strips-1.14482&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;">&#160;</span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="參見"><span id=".E5.8F.83.E8.A6.8B"></span>參見</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=12" title="编辑章节:參見"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E5%8D%81%E8%BF%9B%E4%BD%8D%E5%88%B6" class="mw-redirect" title="十进位制">十進位制</a></li> <li><a href="/wiki/%E5%9C%8B%E9%9A%9B%E5%96%AE%E4%BD%8D%E5%88%B6%E8%A9%9E%E9%A0%AD" class="mw-redirect" title="國際單位制詞頭">國際單位制詞頭</a></li> <li><a href="/wiki/%E4%B8%AD%E6%96%87%E6%95%B8%E5%AD%97" class="mw-redirect" title="中文數字">中文數字</a></li> <li><a href="/w/index.php?title=%E8%8F%AF%E5%9A%B4%E5%A4%A7%E6%95%B8&amp;action=edit&amp;redlink=1" class="new" title="華嚴大數(页面不存在)">華嚴大數</a></li> <li><a href="/wiki/%E5%8D%81%E9%80%B2%E6%99%82" title="十進時">十進時</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="外部連結"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E7.B5.90"></span>外部連結</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8D%81%E8%BF%9B%E5%88%B6&amp;action=edit&amp;section=13" title="编辑章节:外部連結"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080128174347/http://www.nchu.edu.tw/~material/nano/newsbook1.htm">數位名稱自古有之</a></li></ul> <div style="clear: both; height: 1em"></div> <p class="mw-empty-elt"> </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84261037">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output 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.navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em;width:auto;padding-left:0.2em;position:absolute;left:1em}.mw-parser-output .navbox .mw-collapsible-toggle{margin-left:0.5em;position:absolute;right:1em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="进制的记数系统" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Pns" title="Template:Pns"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Pns" title="Template talk:Pns"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:Pns" title="Special:编辑页面/Template:Pns"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="进制的记数系统" style="font-size:110%;margin:0 5em"><a href="/wiki/%E8%BF%9B%E4%BD%8D%E5%88%B6" title="进位制">进制</a>的<a href="/wiki/%E8%AE%B0%E6%95%B0%E7%B3%BB%E7%BB%9F" title="记数系统">记数系统</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">基本进位制</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%B8%80%E8%BF%9B%E5%88%B6" title="一进制">一进制</a></li> <li><a href="/wiki/%E4%BA%8C%E8%BF%9B%E5%88%B6" title="二进制">二进制</a></li> <li><a href="/wiki/%E4%B8%89%E8%BF%9B%E5%88%B6" title="三进制">三进制</a></li> <li><a href="/wiki/%E5%9B%9B%E9%80%B2%E5%88%B6" title="四進制">四进制</a></li> <li><a href="/wiki/%E4%BA%94%E9%80%B2%E5%88%B6" title="五進制">五进制</a></li> <li><a href="/wiki/%E5%85%AD%E8%BF%9B%E5%88%B6" title="六进制">六进制</a></li> <li><a href="/w/index.php?title=%E4%B8%83%E9%80%B2%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="七進制(页面不存在)">七進制</a></li> <li><a href="/wiki/%E5%85%AB%E8%BF%9B%E5%88%B6" title="八进制">八进制</a></li> <li><a href="/wiki/%E4%B9%9D%E9%80%B2%E4%BD%8D" title="九進位">九进制</a></li> <li><a class="mw-selflink selflink">十进制</a></li> <li><a href="/wiki/%E5%8D%81%E4%B8%80%E8%BF%9B%E5%88%B6" title="十一进制">十一进制</a></li> <li><a href="/wiki/%E5%8D%81%E4%BA%8C%E8%BF%9B%E5%88%B6" title="十二进制">十二进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%B8%89%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="十三进制(页面不存在)">十三进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E5%9B%9B%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="十四进制(页面不存在)">十四进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%BA%94%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="十五进制(页面不存在)">十五进制</a></li> <li><a href="/wiki/%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" title="十六进制">十六进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%B8%83%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="十七进制(页面不存在)">十七进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E5%85%AB%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="十八进制(页面不存在)">十八进制</a></li> <li><a href="/w/index.php?title=%E5%8D%81%E4%B9%9D%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="十九进制(页面不存在)">十九进制</a></li> <li><a href="/wiki/%E4%BA%8C%E5%8D%81%E8%BF%9B%E5%88%B6" title="二十进制">二十进制</a></li> <li><a href="/wiki/%E4%BA%8C%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" class="mw-disambig" title="二十六进制">二十六进制</a></li> <li><a href="/wiki/%E4%B8%89%E5%8D%81%E5%85%AD%E8%BF%9B%E5%88%B6" title="三十六进制">三十六进制</a></li> <li><a href="/wiki/%E5%85%AD%E5%8D%81%E9%80%B2%E5%88%B6" title="六十進制">六十进制</a></li> <li><a href="/wiki/%E8%BF%9B%E4%BD%8D%E5%88%B6" title="进位制">六十四进制</a></li> <li><a href="/w/index.php?title=%E4%B8%80%E7%99%BE%E9%80%B2%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="一百進制(页面不存在)">一百进制</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">平衡进位制</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%B9%B3%E8%A1%A1%E4%B8%89%E9%80%B2%E4%BD%8D" title="平衡三進位">平衡三进制</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%B9%BF%E4%B9%89%E7%9A%84%E8%BF%9B%E5%88%B6%E7%B3%BB%E7%BB%9F" title="广义的进制系统">广义的进制系统</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Base64" title="Base64">Base64</a></li> <li><b>十进位制</b>(<a href="#十进位制">章節</a>)</li> <li><a href="/w/index.php?title=%E4%BA%8C%E9%80%B2%E6%8C%87%E6%95%B8%E6%B3%95&amp;action=edit&amp;redlink=1" class="new" title="二進指數法(页面不存在)">二進指數法</a></li> <li><a href="/wiki/%E9%9D%9E%E6%95%B4%E6%95%B0%E8%BF%9B%E4%BD%8D%E5%88%B6" title="非整数进位制">非整数进位制</a> <ul><li><a href="/w/index.php?title=%E6%A0%B9%E5%8F%B72%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="根号2进制(页面不存在)">根號2进制</a></li> <li><a href="/wiki/%E9%BB%84%E9%87%91%E8%BF%9B%E5%88%B6" title="黄金进制">黄金进制</a></li> <li><a href="/wiki/E%E8%BF%9B%E5%88%B6" title="E进制">e进制</a></li></ul></li> <li><span class="ilh-all" data-orig-title="负底数进制" data-lang-code="en" data-lang-name="英语" data-foreign-title="Negative base"><span class="ilh-page"><a href="/w/index.php?title=%E8%B4%9F%E5%BA%95%E6%95%B0%E8%BF%9B%E5%88%B6&amp;action=edit&amp;redlink=1" class="new" title="负底数进制(页面不存在)">负底数进制</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Negative_base" class="extiw" title="en:Negative base"><span lang="en" dir="auto">Negative base</span></a></span>)</span></span></li> <li><a href="/wiki/%E5%A4%8D%E5%BA%95%E6%95%B0%E8%BF%9B%E5%88%B6" title="复底数进制">複底数进制</a> <ul><li><a href="/wiki/2i%E9%80%B2%E5%88%B6" title="2i進制">2i进制</a></li> <li><a href="/wiki/-1%C2%B1i%E8%BF%9B%E5%88%B6" class="mw-redirect" title="-1±i进制">-1±i进制</a></li></ul></li> <li><span class="ilh-all" data-orig-title="混合底數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mixed radix"><span class="ilh-page"><a href="/w/index.php?title=%E6%B7%B7%E5%90%88%E5%BA%95%E6%95%B8&amp;action=edit&amp;redlink=1" class="new" title="混合底數(页面不存在)">混合底數</a></span><span class="noprint ilh-comment">(<span class="ilh-lang">英语</span><span class="ilh-colon">:</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mixed_radix" class="extiw" title="en:Mixed radix"><span lang="en" dir="auto">Mixed radix</span></a></span>)</span></span> <ul><li><a href="/wiki/%E9%98%B6%E4%B9%98%E8%BF%9B%E5%88%B6" title="阶乘进制">阶乘进制</a></li></ul></li> <li><a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E7%BC%96%E7%A0%81" title="斐波那契编码">斐波那契編碼</a></li> <li><a href="/wiki/%E9%9B%99%E5%B0%84%E8%A8%98%E6%95%B8" title="雙射記數">双射记数系统</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">相關條目</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BA%95%E6%95%B0_(%E8%BF%9B%E5%88%B6)" title="底数 (进制)">底数</a></li> <li><a href="/wiki/%E6%95%B0%E4%BD%8D_(%E6%95%B0%E5%AD%A6)" title="数位 (数学)">数位</a></li> <li><a href="/wiki/%E4%BD%8D%E5%85%83" title="位元"> 比特 </a></li> <li><a href="/wiki/%E5%AD%97%E8%8A%82" title="字节">位元組</a></li> <li><a href="/wiki/%E8%BF%9B%E4%BD%8D%E5%88%B6" title="进位制">进位制</a></li> <li><a href="/wiki/%E7%B1%B3%E8%BF%AA%E5%AE%9A%E7%90%86" title="米迪定理">米迪定理</a></li> <li><a href="/wiki/%E8%AE%B0%E6%95%B0%E7%B3%BB%E7%BB%9F" title="记数系统">记数系统</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="分數_&amp;amp;_比率" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="4"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Fractions_and_ratios" title="Template:Fractions and ratios"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Fractions_and_ratios&amp;action=edit&amp;redlink=1" class="new" title="Template talk:Fractions and ratios(页面不存在)"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:Fractions_and_ratios" title="Special:编辑页面/Template:Fractions and ratios"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="分數_&amp;amp;_比率" style="font-size:110%;margin:0 5em"><a href="/wiki/%E5%88%86%E6%95%B8" title="分數">分數</a> &amp; <a href="/wiki/%E7%8E%87" title="率">比率</a></div></th></tr><tr><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0px 2px 0px 0px"><div><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Unicode_0x0025.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Unicode_0x0025.svg/50px-Unicode_0x0025.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Unicode_0x0025.svg/75px-Unicode_0x0025.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Unicode_0x0025.svg/100px-Unicode_0x0025.svg.png 2x" data-file-width="16" data-file-height="16" /></a></span></div></td><th scope="row" class="navbox-group" style="width:1%">除法<br />&比例</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%99%A4%E6%B3%95" title="除法">被除數</a>&#160;: <a href="/wiki/%E5%9B%A0%E6%95%B8" title="因數">除數</a> = <a href="/wiki/%E5%95%86%E6%95%B8" title="商數">商數</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0px 0px 0px 2px"><div><span class="mw-default-size" typeof="mw:File"><span><img alt="The ratio of width to height of standard-definition television." src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Aspect-ratio-4x3.svg/66px-Aspect-ratio-4x3.svg.png" decoding="async" width="66" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Aspect-ratio-4x3.svg/99px-Aspect-ratio-4x3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Aspect-ratio-4x3.svg/131px-Aspect-ratio-4x3.svg.png 2x" data-file-width="139" data-file-height="106" /></span></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">分數</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li>分子/分母=<a href="/wiki/%E5%95%86%E6%95%B8" title="商數">商數</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%BB%A3%E6%95%B8%E5%88%86%E5%BC%8F" title="代數分式">代數</a></li> <li><a href="/wiki/%E9%95%B7%E5%AF%AC%E6%AF%94" title="長寬比">長寬比</a></li> <li><a href="/wiki/%E8%BF%9E%E5%88%86%E6%95%B0" title="连分数">连分数</a></li> <li><a class="mw-selflink selflink">十进制</a></li> <li><a href="/wiki/%E4%BA%8C%E8%BF%9B%E5%88%86%E6%95%B0" title="二进分数">二进分数</a></li> <li><a href="/wiki/%E5%8F%A4%E5%9F%83%E5%8F%8A%E5%88%86%E6%95%B8" title="古埃及分數">古埃及分數</a></li> <li><a href="/wiki/%E9%BB%84%E9%87%91%E5%88%86%E5%89%B2%E7%8E%87" title="黄金分割率">黄金分割率</a> <ul><li><a href="/wiki/%E7%99%BD%E9%8A%80%E6%AF%94%E4%BE%8B" title="白銀比例">白銀比例</a></li></ul></li> <li><a href="/wiki/%E6%95%B4%E6%95%B0" title="整数">整数</a></li> <li><a href="/wiki/%E6%9C%80%E7%AE%80%E5%88%86%E6%95%B0" title="最简分数">最简分数</a> <ul><li><a href="/wiki/%E7%B2%BE%E7%B0%A1" title="精簡">精簡</a></li></ul></li> <li><a href="/wiki/%E6%9C%80%E5%B0%8F%E5%85%AC%E5%88%86%E6%AF%8D" title="最小公分母">最小公分母</a></li> <li><a href="/wiki/%E9%9F%B3%E7%A8%8B" title="音程">音程</a></li> <li><a href="/wiki/%E7%99%BE%E5%88%86%E6%AF%94" title="百分比">百分比</a></li> <li><a href="/wiki/%E5%96%AE%E4%BD%8D%E5%88%86%E6%95%B8" title="單位分數">單位分數</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:%E8%A7%84%E8%8C%83%E6%8E%A7%E5%88%B6" title="Help:规范控制">规范控制数据库</a>:各地 <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q81365#identifiers" title="編輯維基數據鏈接"><img alt="編輯維基數據鏈接" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4149429-5">德国</a></span></li> <li><span class="uid"><a 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