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style="float:right;" class="noprint ws-noexport"> <table width="280px" style="margin:0;margin-left:0.5em;margin-bottom:0.5em;"> <tbody><tr> <td> <table width="100%" border="1" cellpadding="2" cellspacing="0" style="border-collapse:collapse; border-style:1px solid; border-color:#AAAAAA; background-color:#fff; font-size:100%; color:#191919"> <tbody><tr> <th colspan="2" bgcolor="#B0C4DE">Textdaten </th></tr> <tr valign="top" class="hiddenStructure"> <th width="50%" align="left"></th> <th width="50%" align="right"> </th></tr> <tr valign="top"> <td width="40%">Autor:</td> <td width="60%"><b><span id="ws-author">Anonym</span> </b> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Illustrator:</td> <td>{{{ILLUSTRATOR}}} </td></tr> <tr valign="top"> <td>Titel:</td> <td><b><span id="ws-title">Decimalbrüche / Die neuen Maße</span></b> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Untertitel:</td> <td> </td></tr> <tr valign="top"> <td>aus:</td> <td>Beilage des <i>Lesebuchs für die evangelischen Volksschulen Württembergs</i>, 1868 </td></tr> <tr valign="top" class="hiddenStructure"> <td>Herausgeber:</td> <td> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Auflage:</td> <td> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Entstehungsdatum:</td> <td> </td></tr> <tr valign="top"> <td>Erscheinungsdatum:</td> <td><span id="ws-year">1868</span> </td></tr> <tr valign="top"> <td>Verlag:</td> <td><span id="ws-publisher">E. Hallberger</span> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Drucker:</td> <td>{{{DRUCKER}}} </td></tr> <tr valign="top"> <td>Erscheinungsort:</td> <td><span id="ws-place">Stuttgart</span> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Übersetzer:</td> <td><span id="ws-translator"></span> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Originaltitel:</td> <td> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Originalsubtitel:</td> <td> </td></tr> <tr valign="top" class="hiddenStructure"> <td>Originalherkunft:</td> <td> </td></tr> <tr valign="top"> <td>Quelle:</td> <td><span id="ws-scan"><a href="https://commons.wikimedia.org/wiki/File:Die_Ma%C3%9Fe_W%C3%BCrttembergs.png" class="extiw" title="c:File:Die Maße Württembergs.png">Digitalisat auf Commons</a> aus dem „Lesebuch für die evangelischen Volksschulen Württembergs“</span> </td></tr> <tr valign="top"> <td>Kurzbeschreibung:</td> <td>Einführung in die Dezimalbruchrechnung und die neuen metrischen Maße im Königreich Württemberg </td></tr> <tr valign="top" class="hiddenStructure"> <td colspan="2"> </td></tr> <tr valign="top" class="hiddenStructure"> <td colspan="2"><div class="center"><span typeof="mw:File"><a href="/wiki/Datei:Wikipedia-logo-v2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/20px-Wikipedia-logo-v2.svg.png" decoding="async" width="20" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/30px-Wikipedia-logo-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/40px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></a></span> <a href="https://de.wikipedia.org/wiki/" class="extiw" title="w:">Artikel in der Wikipedia</a></div> </td></tr> <tr valign="top" class="hiddenStructure"> <td colspan="2" style="text-align: center;">Eintrag in der <a href="https://de.wikipedia.org/wiki/Gemeinsame_Normdatei" class="extiw" title="w:Gemeinsame Normdatei">GND</a>: <a rel="nofollow" class="external text" href="http://d-nb.info/gnd/{{{GND}}}">{{{GND}}}</a> </td></tr> <tr> <th colspan="2" bgcolor="#f9f9f9">Bild </th></tr> <tr> <td colspan="2"><div class="center"><span typeof="mw:File"><a href="/wiki/Datei:Die_Ma%C3%9Fe_W%C3%BCrttembergs.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Die_Ma%C3%9Fe_W%C3%BCrttembergs.png/250px-Die_Ma%C3%9Fe_W%C3%BCrttembergs.png" decoding="async" width="250" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Die_Ma%C3%9Fe_W%C3%BCrttembergs.png/375px-Die_Ma%C3%9Fe_W%C3%BCrttembergs.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Die_Ma%C3%9Fe_W%C3%BCrttembergs.png/500px-Die_Ma%C3%9Fe_W%C3%BCrttembergs.png 2x" data-file-width="2737" data-file-height="2341" /></a></span></div><span id="ws-cover" style="display:none;">Die Maße Württembergs.png</span> </td></tr> <tr> <th colspan="2" bgcolor="#f9f9f9">Bearbeitungsstand </th></tr> <tr> <td colspan="2" align="center"><span style="color:#669966;"><b>fertig</b></span> </td></tr> <tr> <td colspan="2" style="background-color: #f3f3f3;" align="justify"><div style="font-size:80%; height:auto; color:#669966;"><b>Fertig!</b> Dieser Text wurde zweimal anhand der Quelle <a href="/wiki/Hilfe:Korrekturlesen" title="Hilfe:Korrekturlesen">Korrektur gelesen</a>. Die Schreibweise folgt dem Originaltext.</div> </td></tr> <tr class="hiddenStructure"> <th colspan="2" bgcolor="#f9f9f9"><span style="font-size:85%; color:#009900">Um eine Seite zu bearbeiten, brauchst du nur auf die entsprechende [Seitenzahl] zu klicken. Weitere Informationen findest du hier: <a href="/wiki/Wikisource:Proofread" title="Wikisource:Proofread"><b>Hilfe</b></a></span> </th></tr> <tr class="hiddenStructure"> <th colspan="2" bgcolor="#f9f9f9" align="center"><span id="textdaten_index">[[index:|Indexseite]]</span> </th></tr></tbody></table> </td></tr></tbody></table> </div> <p><br style="clear:all;" /> <span class="ProofRead" style="display:none" title="Die Maße Württembergs.png"> </span> </p> <div style="display:table; text-align:justify; text-indent:0px; padding-left:10px; padding-right:10px;"> <p><span class="PageNumber" id="Seite_Links" style="color: #464646; display: inline; margin: 0px; padding: 0px">[<b>Links</b>]</span> </p> I. <div style="text-align:center"><big><b>Decimalbrüche.</b></big></div> <p>Wie unser Zahlensystem von der Einheit aufsteigt, so daß die Zahlen je auf der nächsten Stelle nach vornen (links) 10mal, also der Einheit gegenüber 10, 100, 1000....mal größer werden; ebenso kann man abwärts steigen, so daß die Zahlen je auf der nächsten Stelle nach hinten (rechts) 10mal, also der Einheit gegenüber 10, 100, 1000....mal kleiner werden. Dieses gleichmäßige Auf- und Absteigen stellt folgende Tabelle dar: </p> <div style="overflow:scroll"> <table border="2" cellspacing="0" cellpadding="4" rules="all" style="margin:0em 0em 1em 0em; border:solid 1px #AAAAAA; border-collapse:collapse; background-color:#F9F9F9; font-size:95%; empty-cells:show; color:black;"> <tbody><tr> <td><small>u.s.w</small> </td> <td><small>Millionen.</small> </td> <td><small>Hundert-<br />Tausender.</small> </td> <td><small>Zehn-<br />Tausender.</small> </td> <td><small>Tausender.</small> </td> <td><small>Hunderter.</small> </td> <td><small>Zehne.r</small> </td> <td><small><b>Einheit.</b></small> </td> <td><small>Zehntel.</small> </td> <td><small>Hundertel</small> </td> <td><small>Tausendtel.</small> </td> <td><small>Zehn-<br />Tausendtel.</small> </td> <td><small>Hundert-<br />Tausendtel.</small> </td> <td><small>Milliontel.</small> </td> <td><small>u.s.w</small> </td></tr> <tr> <td> </td> <td>VII. </td> <td>VI. </td> <td>V. </td> <td>IV. </td> <td>III. </td> <td>II. </td> <td>I. </td> <td>II. </td> <td>III. </td> <td>IV. </td> <td>V. </td> <td>VI. </td> <td>VII. </td> <td> </td></tr></tbody></table> </div> <p>Solche Zehntels Theil- oder Bruchzahlen heißen Decimalbrüche, d. h. zehntheilige Brüche. Die Grenze zwischen den ganzen Zahlen und den Bruchzahlen bezeichnet man durch , oder . z.B. 7,4 oder 7.4. Die Stelle der Einer muß immer angegeben werden, wenn keine Ganzen da sind durch 0; z. B. 3,46. 0,45. Die Bruchzahlen werden gelesen wie ganze Zahlen und dazu spricht man blos den größten Nenner aus, welcher stets 1 ist mit so vielen Nullen, als Decimalstellen vorhanden sind; z. B. 0,127 = 127/1000, 127 Tausendtel; 0,0204 = 204 Zehntausendtel.<br /> Durch Verrücken des Decimalzeichens nach rechts oder links werden die Zahlen 10, 100, 1000...mal größer oder kleiner, weil dadurch die Zahlen auf die Stelle der Zehner, Hunderter, Tausender u.s.w. hinaufgerückt oder auf die Stelle der Zehntel, Hundertel. Tausendtel u. s. w. hinabgesetzt werden.<br /> Die Rechenoperationen werden mit Decimalbrüchen ganz so vorgenommen, als hätte man ganze Zahlen.<br /> 1. 2. Beim Addiren und Subtrahiren setze man sorgfältig die gleichnamigen Stellen unter einander und im Resultat auch wieder das Decimalzeichen an seinem Platz.<br /> </p> <div style="text-align:center"><i>z. B. 1)</i> <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{array}{rr}&3,276\\&0,859\\\hline &\ 4,135.\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right right" rowspacing="4pt" columnspacing="1em" rowlines="none solid"> <mtr> <mtd /> <mtd> <mn>3</mn> <mo>,</mo> <mn>276</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mn>0</mn> <mo>,</mo> <mn>859</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mtext> </mtext> <mn>4</mn> <mo>,</mo> <mn>135.</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{rr}&3,276\\&0,859\\\hline &\ 4,135.\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b051a597de88ead05cc95e48b079d71628171ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:11.843ex; height:10.176ex;" alt="{\displaystyle {\begin{array}{rr}&3,276\\&0,859\\\hline &\ 4,135.\end{array}}}"></span> <i>2)</i><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{array}{rr}&3,276\\&0,859\\\hline &\ 2,417.\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right right" rowspacing="4pt" columnspacing="1em" rowlines="none solid"> <mtr> <mtd /> <mtd> <mn>3</mn> <mo>,</mo> <mn>276</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mn>0</mn> <mo>,</mo> <mn>859</mn> </mtd> </mtr> <mtr> <mtd /> <mtd> <mtext> </mtext> <mn>2</mn> <mo>,</mo> <mn>417.</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{array}{rr}&3,276\\&0,859\\\hline &\ 2,417.\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22171042ff182b716d093e37d1f524501d553c2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:11.843ex; height:10.176ex;" alt="{\displaystyle {\begin{array}{rr}&3,276\\&0,859\\\hline &\ 2,417.\end{array}}}"></span></div><br /> <p>3. Beim Multipliciren werden im Resultat so viele Decimalstellen angegeben, als beide Factoren zusammen haben; z. B.<br /> </p> <div style="text-align:center"><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 327\cdot 2,31=755,37.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>327</mn> <mo>⋅</mo> <mn>2</mn> <mo>,</mo> <mn>31</mn> <mo>=</mo> <mn>755</mn> <mo>,</mo> <mn>37.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 327\cdot 2,31=755,37.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bd3e3b7e06f1d224437626f40878540c58c5214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.279ex; height:2.509ex;" alt="{\displaystyle 327\cdot 2,31=755,37.}"></span>   <p><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 32,7\cdot 2,31=75,537.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>32</mn> <mo>,</mo> <mn>7</mn> <mo>⋅</mo> <mn>2</mn> <mo>,</mo> <mn>31</mn> <mo>=</mo> <mn>75</mn> <mo>,</mo> <mn>537.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 32,7\cdot 2,31=75,537.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7793b8be9549f99605ee36e2151d31d8f5ddd99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.313ex; height:2.509ex;" alt="{\displaystyle 32,7\cdot 2,31=75,537.}"></span> <br /> <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 3,27\cdot 2,31=7,5537.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>,</mo> <mn>27</mn> <mo>⋅</mo> <mn>2</mn> <mo>,</mo> <mn>31</mn> <mo>=</mo> <mn>7</mn> <mo>,</mo> <mn>5537.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3,27\cdot 2,31=7,5537.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13c5018d6bad1f40f619002e131abe0adaa77e54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.313ex; height:2.509ex;" alt="{\displaystyle 3,27\cdot 2,31=7,5537.}"></span>   <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 0,327\cdot 2,31=0,75537.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>,</mo> <mn>327</mn> <mo>⋅</mo> <mn>2</mn> <mo>,</mo> <mn>31</mn> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>75537.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0,327\cdot 2,31=0,75537.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d1edeb2ad7140907ea2f0c3d88d0df2dc13c616" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.638ex; height:2.509ex;" alt="{\displaystyle 0,327\cdot 2,31=0,75537.}"></span> <br /> </p> <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 0,327\cdot 0,231=0,075537.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>,</mo> <mn>327</mn> <mo>⋅</mo> <mn>0</mn> <mo>,</mo> <mn>231</mn> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>075537.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0,327\cdot 0,231=0,075537.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1384c0443b0a451c6fb4e8757ec368a2afb14906" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.963ex; height:2.509ex;" alt="{\displaystyle 0,327\cdot 0,231=0,075537.}"></span></div><br /> 4. Beim Dividiren mache zuerst die Anzahl der Decimalstellen in beiden Zahlen gleich (durch Anhängung von Nullen an die Zahl mit weniger Decimalstellen) z. B.<br /> <div style="text-align:center"><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 2\div 3,27=2,00\div 3,27.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>27</mn> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>00</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>27.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\div 3,27=2,00\div 3,27.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d65459ce37e23dcfb70a0cc7a1ca4f4955ba868" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.152ex; height:2.509ex;" alt="{\displaystyle 2\div 3,27=2,00\div 3,27.}"></span>   <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 2,4\div 3,27=2,40\div 3,27}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>,</mo> <mn>4</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>27</mn> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>40</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>27</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2,4\div 3,27=2,40\div 3,27}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad4ee11dd990b03cdd636b799c7146e5106a0a3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:25.702ex; height:2.509ex;" alt="{\displaystyle 2,4\div 3,27=2,40\div 3,27}"></span>; <br /> <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 2,405\div 3,27=2,405\div 3,270}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>,</mo> <mn>405</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>27</mn> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>405</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>270</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2,405\div 3,27=2,405\div 3,270}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/671904622bc87a6b3244263b1300d7ec5608d513" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:30.352ex; height:2.509ex;" alt="{\displaystyle 2,405\div 3,27=2,405\div 3,270}"></span></div> und verfahre dann wie mit ganzen Zahlen;<br /> <p>der Quotient bekommt also ein Decimalzeichen erst, wenn auch der Rest (mittelst Anhängung von Nullen) decimal berechnet wird, z. B.:<br /> </p> <div style="text-align:center"><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 3,2\div 9,6=3.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo>÷</mo> <mn>9</mn> <mo>,</mo> <mn>6</mn> <mo>=</mo> <mn>3.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3,2\div 9,6=3.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a07ad632e822acd3d7ada012e851d04d8bbdf4a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.466ex; height:2.509ex;" alt="{\displaystyle 3,2\div 9,6=3.}"></span>   <p><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 3,2\div 7,5=2,34.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo>÷</mo> <mn>7</mn> <mo>,</mo> <mn>5</mn> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>34.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3,2\div 7,5=2,34.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887808e2fa907e06298d8917b8a80106036e2fa0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.825ex; height:2.509ex;" alt="{\displaystyle 3,2\div 7,5=2,34.}"></span> <br /> </p> <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 7,5\div 3,2=0,426.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>7</mn> <mo>,</mo> <mn>5</mn> <mo>÷</mo> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>426.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 7,5\div 3,2=0,426.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b11df8a22faffa8a3b0149d2eb5306581ce0a3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.987ex; height:2.509ex;" alt="{\displaystyle 7,5\div 3,2=0,426.}"></span></div><br /> <p><span class="PageNumber" id="Seite_Rechts" style="color: #464646; display: inline; margin: 0px; padding: 0px">[<b>Rechts</b>]</span> </p> <div style="text-align:center"><big><b>Die neuen Maße.</b></big></div> <p>Beim kommenden neuen Maßsystem sollen die Grundmaße werden: </p><p>1) für’s Längenmaß <b>der Meter</b> (m), ein wenig kleiner als <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 3\textstyle {\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\textstyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71d6ccc7d971588a8d3ed75f09f48459a9730698" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.821ex; height:3.509ex;" alt="{\displaystyle 3\textstyle {\frac {1}{2}}}"></span> württb.. Fuß (3,49’); 1 Fuß = 0,286 m. Dieses Längenmaß wird angewendet </p> <dl><dd>a. auf Flächen (mit Länge und Breite); das gibt Quadratmeter (m oder qm.)</dd> <dd>b. auf Körper (mit Länge, Breite und Höhe); das gibt Cubikmeter (cbm.) Ein Cubikdecimeter ist gleich einem Liter s. Nr. 2).</dd> <dd>c. bei Anwendung des Flächenmaßes auf die Feldmessung legt man zu Grunde den Ar, d.h. 100m (Quadratmeter), das ist gleich einem Quadrat auf dem 10fachen Meter, und den Hectar, d. h. ein Quadrat auf dem 100fachen Meter = 10,000 m.</dd></dl> <p>2) Das Grundmaß für Hohlmaße ist der (oder das) <b>Liter</b> (l.), nicht ganz <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 2\textstyle {\frac {1}{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\textstyle {\frac {1}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62d110c71fe85e106c8a455ef6af1cc2668c79eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.821ex; height:3.676ex;" alt="{\displaystyle 2\textstyle {\frac {1}{6}}}"></span> (2,1777..) württb.Schoppen; 1 Schopp. = 0,46 l.; 1 Imi = 18,371.; 1 Eimer = 293,93 l.; 1 Scheffel = 177 l.; 1 Sri. = 22 l.; 1 Bierl. = 5,5 l.; (1 cbm. = 1 Kiloliter = 3,4 Eimer oder 5 Schfl. 5 Sri.) </p><p>3.) für’s Gewicht – das <b>Gramm</b> (g.), ungefähr <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 \textstyle {\frac {1}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a74a4015e5e0820e4ab2523bef1064fdfcf225d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\displaystyle \textstyle {\frac {1}{4}}}"></span> württb. Quint, so daß 1000 Gramm (1 Kilogramm) genau zwei jetztige Pfunde geben; 1 Loth = 15,62 g. 1 Pfd. = 500 g. 1 Centner 50 Kilogramm. </p><p>Diese Grundmaße werden je ums Zehnfache vergrößert oder verkleinert und zwar bedeutet </p> <table border="2" cellspacing="0" cellpadding="4" rules="all" style="margin:0em 0em 1em 0em; border:solid 1px #AAAAAA; border-collapse:collapse; background-color:#F9F9F9; font-size:95%; empty-cells:show; color:black; {{{1}}}"> <tbody><tr> <td>Deka =</td> <td>das Zehnfache vom</td> <td>g. l. m., z. B.</td> <td>Dekamter = 10 m. </td></tr> <tr> <td>Hecto =</td> <td>das Hundertfache „</td> <td>g. l. m., „ „</td> <td>Hectoliter = 100 l. </td></tr> <tr> <td>Kilo =</td> <td>das Tausendfache „</td> <td>g. l. m., „ „</td> <td>Kilogramm = 1000 g. </td></tr> <tr> <td>(Myria =</td> <td>das Zehntausendfache „</td> <td>g. l. m., „ „</td> <td>Myriameter = 10,000 m. </td></tr> <tr> <td>Deci =</td> <td>ein Zehntel „</td> <td>g. l. m., „ „</td> <td>Decigramm = <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 \textstyle {\frac {1}{10}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>10</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{10}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99b2a631124308e27e35e78162e901bae97fe317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.48ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{10}}}"></span> g. </td></tr> <tr> <td>Centi =</td> <td>ein Hundertel „</td> <td>g. l. m., „ „</td> <td>Centiliter = <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 \textstyle {\frac {1}{100}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>100</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{100}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9728821ce55fdbf935175f93f0c541522675c138" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:3.302ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{100}}}"></span> l. </td></tr> <tr> <td>Milli =</td> <td>ein Tausendtel. „</td> <td>g. l. m., „ „</td> <td>Millimeter = <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 \textstyle {\frac {1}{1000}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>1000</mn> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{1000}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ebada42a3aef1186122573d00d5da8f2c055632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:4.124ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{1000}}}"></span> m. </td></tr></tbody></table> <p>Durch bloße Vorrückung des Decimalzeichens können die verschiedenen Maßabstufungen in einander verwandelt werden. Z. B. 325 m. = 3 Hectometer, 2 Decameter, 5 Meter; 32,5 m. = 3 Dekameter, 2 Meter, 5 Decimeter. 3,25 m. = 3 Meter, 2 Decimeter, 5 Centimeter. 0,325 m. = 3 Decimeter, 2 Centimeter, 5 Millimeter. Umgekehrt gehts durch Zurücksetzen des Decimalzeichens, z.B. 0,325 m. = 3 Decimeter, 2 Centimeter, 5 Millimeter. 3,25 m. = 3 Meter, 2 Decimeter, 5 Centimeter; 32,5 m. 3 Dekameter, 2 Meter, 5 Decimeter; 325,0 m. = 3 Hectometer, 2 Dekameter, 5 Meter. </p> <center><b>Die einfachsten Brüche in Decimalbrüchen ausgedrückt:</b></center> <p><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 \textstyle {\frac {1}{2}}=0,5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>5</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{2}}=0,5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a7290aa0aaeb210dccf8a582d8e0cebb405f552" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:8.115ex; height:3.509ex;" alt="{\displaystyle \textstyle {\frac {1}{2}}=0,5}"></span>; <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 \textstyle {\frac {1}{3}}=0,333{\text{..}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>333</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>..</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{3}}=0,333{\text{..}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4d6a2ffc69df730019bdb2db894a89422eed90f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.734ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{3}}=0,333{\text{..}}}"></span>; <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 \textstyle {\frac {1}{4}}=0,25}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>25</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{4}}=0,25}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d37b64e8a3002b699f13c24f6b4d2cb604c5c261" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.278ex; height:3.509ex;" alt="{\displaystyle \textstyle {\frac {1}{4}}=0,25}"></span>; <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 \textstyle {\frac {3}{4}}=0,75}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>75</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {3}{4}}=0,75}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/582eba1a9dcb0c5260646296739f437a5c85a814" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.278ex; height:3.509ex;" alt="{\displaystyle \textstyle {\frac {3}{4}}=0,75}"></span>; <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 \textstyle {\frac {1}{5}}=0,2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{5}}=0,2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b23a934e1da760fa0ba0d07a56534fc6fac9eb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:8.115ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{5}}=0,2}"></span>; <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 \textstyle {\frac {1}{6}}=0,166{\text{.}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>166</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>.</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{6}}=0,166{\text{.}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07a3b35bb82033b3e008028321e1430ccdab8560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.087ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{6}}=0,166{\text{.}}}"></span>; <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 \textstyle {\frac {1}{7}}=0,143{\text{..}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>7</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>143</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>..</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{7}}=0,143{\text{..}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/562f0a9222705171fbb627fe19593fb857ddef48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.734ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{7}}=0,143{\text{..}}}"></span>; <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 \textstyle {\frac {1}{8}}=0,125}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>125</mn> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{8}}=0,125}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af31c439dff33df39ced5fbc8df0f54013016164" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.44ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{8}}=0,125}"></span>; <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 \textstyle {\frac {1}{9}}=0,111{\text{....}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>9</mn> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>111</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext>....</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {\frac {1}{9}}=0,111{\text{....}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/516f7d4fa026e142938395d47f71b8f26c6d6ac1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:13.028ex; height:3.676ex;" alt="{\displaystyle \textstyle {\frac {1}{9}}=0,111{\text{....}}}"></span><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> </div> <div class="mw-heading mw-heading2"><h2 id="Anmerkungen_(Wikisource)"><span id="Anmerkungen_.28Wikisource.29"></span>Anmerkungen (Wikisource)</h2></div> <div style="font-size:90%;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Gleichheitszeichen ergänzt</span> </li> </ol></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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