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273 lines
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HTML
273 lines
10 KiB
HTML
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Convert Fractions to Decimals</h1>
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<div style="background: url(numbers/images/hdr-screws-tape.jpg) no-repeat; width: 100%; height: 100px; background-position: center center;"></div>
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<h3>The simplest method is to use a calculator.</h3>
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<p>Just divide the top of the fraction by the bottom, and read off the answer!</p>
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<div class="example">
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<h3>Example<i>:</i> What is <span class="intbl">
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<em>5</em>
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<strong>8</strong>
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</span> as a decimal ... ?</h3>
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<p style="float:left; margin: 0 10px 5px 0;"><a href="scientific-calculator.html"><img src="images/calculator.gif" alt="calculator" height="97" width="76"></a></p>
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<p class="center larger">... get your calculator and type in "5 / 8 ="</p>
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<p>The answer should be <b>0.625</b></p>
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</div>
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<h3>No Calculator? Use <a href="long_division3.html">Long Division to Decimal Places</a></h3>
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<div class="example">
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<h3>Example: here is what long division of <span class="intbl">
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<em>5</em>
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<strong>8</strong>
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</span> looks like:</h3>
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<br>
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<div class="mono">
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<span style="border-bottom: 1px solid;"> 0.625</span><br>
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8 )5.000<br>
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<span style="border-bottom: 1px solid;">0</span><br>
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5.0<br>
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<span style="border-bottom: 1px solid;">4.8</span><br>
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20<br>
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<span style="border-bottom: 1px solid;">16</span><br>
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40<br>
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<span style="border-bottom: 1px solid;">40</span><br>
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0
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</div>
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<p>In that case we inserted extra zeros and did <span class="intbl"> <em>5.000</em> <strong>8</strong> </span> to get <b>0.625</b></p>
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<p>Read the <a href="long_division3.html">Long Division to Decimal Places</a> page for more details.</p>
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</div>
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<h2>Another Method</h2>
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<h3>Yet another method you may like is to follow these steps:</h3>
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<ul>
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<li><b>Step 1</b>: Find a number you can multiply by <b>the bottom of the fraction</b> to make it 10, or 100, or 1000, or any <font color="blue">1 followed by 0s</font>.</li>
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<li><b>Step 2</b>: Multiply both top and bottom by that number.</li>
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<li><b>Step 3</b>. Then write down just the top number, putting the decimal point in the correct spot (one space
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from the right hand side for every zero in the bottom number)</li>
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</ul>
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<div class="example">
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<h3>Example: Convert <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span> to a Decimal</h3>
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<p>Step 1: We can multiply 4 by <span class="large">25</span> to become 100</p>
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<p>Step 2: Multiply top and bottom by 25:</p>
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<div class="clear">
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<table class="larger" align="center" cellspacing="5" cellpadding="0" border="0">
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<tbody>
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<tr style="text-align:center;">
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<td colspan="3"><b>×25</b></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="25" width="75"></td>
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</tr>
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<tr class="larger" align="center">
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<td><span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span></td>
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<td> = </td>
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<td><span class="intbl">
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<em>75</em>
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<strong>100</strong>
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</span></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="25" width="75"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><b>×25</b></td>
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</tr>
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</tbody></table>
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</div>
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<p>Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);</p>
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<p class="center large">Answer = 0.75</p>
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</div>
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<div class="example">
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<h3>Example: Convert <span class="intbl">
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<em>3</em>
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<strong>16</strong>
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</span> to a Decimal</h3>
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<p>Step 1: We have to multiply 16 by <b>625</b> to become 10,000</p>
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<p>Step 2: Multiply top and bottom by 625:</p>
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<div class="clear">
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<table class="larger" align="center" cellspacing="5" cellpadding="0" border="0">
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<tbody>
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<tr style="text-align:center;">
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<td colspan="3"><b>×625</b></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="25" width="75"></td>
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</tr>
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<tr class="larger" align="center">
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<td><span class="intbl">
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<em>3</em>
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<strong>16</strong>
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</span></td>
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<td> = </td>
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<td><span class="intbl">
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<em>1,875</em>
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<strong>10,000</strong>
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</span></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="25" width="75"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><b>×625</b></td>
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</tr>
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</tbody></table>
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</div>
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<p>Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);</p>
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<p class="center"><span class="large">Answer = 0.1875</span></p>
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</div>
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<div class="example">
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<h3>Example: Convert <span class="intbl">
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<em>1</em>
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<strong>3</strong>
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</span> to a Decimal</h3>
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<p>Step 1: There is no way to multiply 3 to become 10 or 100 or any "1 followed by 0s", but we can calculate an <b>approximate</b> decimal by choosing
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to multiply by, say, 333</p>
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<p>Step 2: Multiply top and bottom by 333:</p>
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<div class="clear">
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<table class="larger" align="center" cellspacing="5" cellpadding="0" border="0">
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<tbody>
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<tr style="text-align:center;">
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<td colspan="3"><b>×333</b></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="25" width="75"></td>
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</tr>
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<tr class="larger" align="center">
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<td><span class="intbl">
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<em>1</em>
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<strong>3</strong>
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</span></td>
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<td> = </td>
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<td><span class="intbl">
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<em>333</em>
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<strong>999</strong>
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</span></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="25" width="75"></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3"><b>×333</b></td>
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</tr>
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</tbody></table>
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</div>
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<p>Step 3: Now, <b>999 is <i>nearly</i> 1,000</b>, so let us write down 333 with the decimal point 3 spaces from the right (because 1,000 has 3 zeros):</p>
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<p class="center large">Answer = 0.333 (accurate to only 3 decimal places !!)</p>
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</div><p> </p>
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<div class="questions">947, 1362, 948, 1361, 3487, 3488, 1363, 3489, 3490, 3491</div>
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<div class="related">
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<a href="fractions.html">Introduction to Fractions</a>
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<a href="decimals.html">Introduction to Decimals</a>
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<a href="converting-decimals-fractions.html">Convert Decimals to Fractions</a>
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<a href="converting-fractions-percents.html">Convert Fractions to Percents</a>
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<a href="equivalent_fractions.html">Equivalent Fractions</a>
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<a href="simplifying-fractions.html">Simplifying Fractions</a>
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<a href="fractions-menu.html">Fractions Index</a>
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<a href="decimals-menu.html">Decimals Index</a>
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</div>
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