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214 lines
8.8 KiB
HTML
214 lines
8.8 KiB
HTML
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<title>Multiplying Decimals</title>
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<body id="bodybg">
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<div class="bg">
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Multiplying Decimals</h1>
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<p align="center"><i>Multiply without the decimal point, then re-insert it in the correct spot!</i></p>
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<h2>How to Multiply Decimals</h2>
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<p>Just follow these steps:</p>
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<ul>
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<li>Multiply normally, ignoring the decimal points.</li>
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<li><b>Then</b> put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.</li>
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</ul>
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<p>In other words, just count up how many numbers are after the decimal point in <i>both</i> numbers you are multiplying, then the answer should have that many numbers after <i>its</i> decimal point. </p>
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<p> </p>
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<div class="example">
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<h3>Example: Multiply 0.03 by 1.1</h3>
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<table border="0" align="center">
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<tr>
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<td><div align="right">start with:</div></td>
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<td width="20"> </td>
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<td nowrap><b>0.03 × 1.1</b></td>
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</tr>
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<tr>
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<td><div align="right">multiply without decimal points:</div></td>
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<td> </td>
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<td nowrap><b>3 × 11 = 33</b></td>
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</tr>
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<tr>
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<td><div align="right">0.03 has <b>2 decimal places</b>,<br />
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and 1.1 has <b>1 decimal place</b>, <br />
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so the answer has <b>3 decimal places</b>:</div></td>
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<td> </td>
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<td valign="bottom" nowrap><b>0.033</b></td>
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</tr>
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</table>
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</div>
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<p> </p>
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<div class="simple">
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<table border="0" align="center">
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<tr>
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<td><img src="images/style/animation.gif" alt="animation" width="70" height="43" /></td>
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<td>See the <a href="numbers/decimals-multiplying-animation.html">Multiplying Decimals Animations</a></td>
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</tr>
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</table>
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</div>
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<h2>How Does It Work?</h2>
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<p>Because when you multiply without the decimal point, you are really shifting the decimal point to the right to <b>get it out of the way</b>:</p>
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<div class="clear">
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<table border="0" align="center">
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<tr align="center">
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<td><i>Original:</i></td>
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<td><i></i></td>
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<td><i>1 Move:</i></td>
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<td><i></i></td>
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<td><i>2 Moves:</i></td>
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<td><i></i></td>
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<td><i>3 Moves:</i></td>
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</tr>
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<tr align="center">
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<td>0.03 × 1.1</td>
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<td> <img src="images/arrow.gif" width="30" height="30" alt="arrow" /> </td>
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<td><b>0.3</b> × 1.1</td>
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<td> <img src="images/arrow.gif" width="30" height="30" alt="arrow" /> </td>
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<td><b>3.</b> × 1.1</td>
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<td> <img src="images/arrow.gif" width="30" height="30" alt="arrow" /> </td>
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<td><b>3.</b> ×<b> 11.</b></td>
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</tr>
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</table>
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</div>
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<p>Then we do the (now easy) multiplication:</p>
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<p align="center" class="large">3. × 11. = 33.</p>
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<p>But remember, we did 3 Moves of the decimal point, so we need to undo that:</p>
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<table border="0" align="center">
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<tr align="center">
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<td><i>3 Moves:</i></td>
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<td><i></i></td>
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<td><i>2 Moves:</i></td>
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<td><i></i></td>
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<td><i>1 Move:</i></td>
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<td><i></i></td>
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<td><i>Correct</i></td>
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</tr>
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<tr align="center">
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<td><b>33.</b></td>
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<td><img src="images/arrow.gif" width="30" height="30" alt="arrow" /></td>
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<td><b>3.3</b></td>
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<td><img src="images/arrow.gif" width="30" height="30" alt="arrow" /></td>
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<td><b>0.33</b></td>
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<td><img src="images/arrow.gif" width="30" height="30" alt="arrow" /></td>
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<td><b>0.033</b></td>
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</tr>
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</table>
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<p>Here are some more examples:</p>
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<div class="example">
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<h3>Example: Multiply 0.25 by 0.2</h3>
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<div class="clear">
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<table border="0" align="center">
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<tr>
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<td><div align="right">start with:</div></td>
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<td> </td>
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<td nowrap><b>0.25 × 0.2</b></td>
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</tr>
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<tr>
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<td><div align="right">multiply without decimal points:</div></td>
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<td> </td>
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<td nowrap><b>25 × 2 = 50</b></td>
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</tr>
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<tr>
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<td><div align="right">0.25 has <b>2</b> decimal places,<br />
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and 0.2 has <b>1</b> decimal place, <br />
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so the answer has <b>3</b> decimal places:</div></td>
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<td> </td>
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<td valign="bottom" nowrap><b>0.050</b></td>
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</tr>
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</table>
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</div>
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</div>
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<div class="example">
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<h3>Example: Multiply 102 by 0.22</h3>
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<div class="clear">
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<table border="0" align="center">
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<tr>
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<td><div align="right">start with:</div></td>
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<td> </td>
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<td nowrap><b>102 × 0.22</b></td>
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</tr>
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<tr>
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<td><div align="right">multiply without decimal points:</div></td>
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<td> </td>
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<td nowrap><b>102 × 22 = 2244</b></td>
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</tr>
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<tr>
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<td><div align="right">102 has <b>0</b> decimal places,<br />
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and 0.22 has <b>2</b> decimal place, <br />
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so the answer has <b>2</b> decimal places:</div></td>
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<td> </td>
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<td valign="bottom" nowrap><b>22.44</b></td>
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</tr>
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</table>
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</div>
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</div>
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<h2>Common Sense</h2>
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<p>As a final check you can put your "common sense" hat on and think <b><i>"is that the right size?"</i></b>, because you don't want to pay ten times too much for anything, nor get only one-tenth of what you need!</p>
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<p> And that's all. </p>
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<p class="center80">Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.</p><p> </p>
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<div class="questions"><a href="worksheets/decimals.html">Decimal Worksheets</a><br />
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<script type="text/javascript">getQ(962, 1348, 963, 1349, 964, 1350, 3463, 3464, 3465, 3466);</script>
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</div>
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<div class="related"> <a href="decimals.html">Decimals</a> <a href="decimals-menu.html">Decimals Index</a> <a href="worksheets/decimals.html">Decimal Worksheets</a> <a href="adding-decimals.html">Adding Decimals</a> <a href="subtracting-decimals.html">Subtracting Decimals</a> <a href="dividing-decimals.html">Dividing Decimals</a> <a href="index-notation-powers.html">Powers of 10</a> </div>
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Copyright © 2017 MathsIsFun.com
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