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394 lines
14 KiB
HTML
394 lines
14 KiB
HTML
<!doctype html>
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<html lang="en">
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<!-- Mirrored from www.mathsisfun.com/converting-decimals-fractions.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:36:23 GMT -->
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<head>
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<meta charset="UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Convert Decimals to Fractions</title>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<header>
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<div id="cookOK"></div>
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</header>
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Convert Decimals to Fractions</h1>
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<div style="background: url(numbers/images/hdr-cut-bread.jpg) no-repeat; width: 100%; height: 80px; background-position: center center;"></div>
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<h3>To convert a Decimal to a Fraction follow these steps:</h3>
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<ul>
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<li><b>Step 1:</b> Write down the decimal divided by 1, like this: <span class="large"><span class="intbl">
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<em>decimal</em>
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<strong>1</strong>
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</span></span></li>
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<li><b>Step 2:</b> Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)</li>
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<li><b>Step 3:</b> <a href="simplifying-fractions.html">Simplify</a> (or reduce) the fraction</li>
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</ul>
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<div class="example">
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<h3>Example: Convert 0.75 to a fraction</h3>
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<p><b>Step 1:</b> Write down 0.75 divided by 1:</p>
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<p class="center larger"><span class="intbl">
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<em>0.75</em>
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<strong>1</strong>
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</span></p>
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<p><b>Step 2:</b> Multiply both top and bottom by <b>100</b> (because there are 2 digits after the decimal point so that is 10×10=100):</p>
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<table align="center" border="0" cellspacing="5" cellpadding="0">
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<tr style="text-align:center;">
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<td colspan="3">× 100</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="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;" class="larger">
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<td><span class="intbl">
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<em>0.75</em>
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<strong>1</strong>
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</span></td>
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<td style="width:30px;">=</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="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3">× 100</td>
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</tr>
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</table>
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<div class="center">
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<p><i>(Do you see how it turns the top number<br>
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into a whole number?)</i></p>
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</div>
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<p><b>Step 3:</b> <a href="simplifying-fractions.html">Simplify the fraction</a> (this took me two steps):</p>
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<table align="center" border="0" cellspacing="5" cellpadding="0">
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<tr style="text-align:center;">
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<td style="text-align:center;"> </td>
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<td style="width:45px;">÷5</td>
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<td> </td>
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<td style="width:45px;">÷ 5</td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="5" align="center"><img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="30" width="79" > <img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;" class="larger">
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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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<td style="width:45px;">=</td>
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<td><span class="intbl">
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<em>15</em>
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<strong>20</strong>
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</span></td>
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<td style="width:45px;">=</td>
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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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</tr>
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<tr style="text-align:center;">
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<td colspan="5" align="center"><img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="30" width="79" > <img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;">
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<td style="text-align:center;"> </td>
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<td style="width:45px;">÷5</td>
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<td> </td>
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<td style="width:45px;">÷ 5</td>
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<td> </td>
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</tr>
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</table>
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<p> </p>
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<h3 align="center">Answer = <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span></h3>
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<p> </p>
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<div class="center">
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<p><i>Note: 75/100 is called a <b>decimal fraction</b> and 3/4 is called a <b>common fraction</b> !</i></p>
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</div>
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</div>
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<div class="example">
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<h3>Example: Convert 0.625 to a fraction</h3>
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<p><b>Step 1:</b> write down:</p>
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>0.625</em>
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<strong>1</strong>
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</span></p>
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</div>
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<p><b>Step 2:</b> multiply both top and bottom by <b>1,000</b> (3 digits after the decimal point, so 10×10×10=1,000)</p>
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>625</em>
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<strong>1000</strong>
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</span></p>
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</div>
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<p><b>Step 3:</b> Simplify the fraction (it took me two steps here):</p>
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<table align="center" border="0" cellspacing="5" cellpadding="0">
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<tr style="text-align:center;">
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<td style="text-align:center;"> </td>
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<td>÷ 25</td>
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<td> </td>
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<td>÷ 5</td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="5" align="center"><img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="30" width="79" > <img src="images/style/arrow-rt-over.svg" alt="right over arrow" height="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;" class="larger">
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<td><span class="intbl">
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<em>625</em>
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<strong>1000</strong>
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</span></td>
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<td style="width:30px;">=</td>
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<td><span class="intbl">
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<em>25</em>
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<strong>40</strong>
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</span></td>
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<td style="width:30px;">=</td>
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<td><span class="intbl">
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<em>5</em>
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<strong>8</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="5" align="center"><img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="30" width="79" > <img src="images/style/arrow-rt-under.svg" alt="right under arrow" height="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;">
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<td> </td>
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<td>÷ 25</td>
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<td> </td>
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<td>÷ 5</td>
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<td> </td>
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</tr>
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</table>
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<p> </p>
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<h3 align="center">Answer = <span class="intbl">
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<em>5</em>
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<strong>8</strong>
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</span></h3>
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</div>
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<p>When there is a whole number part, put the whole number aside and bring it back at the end:</p>
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<div class="example">
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<h3>Example: Convert 2.35 to a fraction</h3>
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<p class="larger"><b>Put the 2 aside and just work on 0.35</b></p>
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<p><b>Step 1:</b> write down:</p>
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>0.35</em>
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<strong>1</strong>
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</span></p>
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</div>
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<p><b>Step 2:</b> multiply both top and bottom by <b>100</b> (2 digits after the decimal point so that is 10×10=100):</p>
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>35</em>
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<strong>100</strong>
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</span></p>
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</div>
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<p><b>Step 3:</b> Simplify the fraction:</p>
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<table align="center" border="0" cellspacing="5" cellpadding="0" class="larger">
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<tr style="text-align:center;">
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<td colspan="3">÷ 5</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="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;" class="larger">
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<td><span class="intbl">
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<em>35</em>
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<strong>100</strong>
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</span></td>
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<td style="width:30px;">=</td>
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<td><span class="intbl">
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<em>7</em>
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<strong>20</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="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3">÷ 5</td>
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</tr>
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</table>
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<p><b class="larger">Bring back the 2</b> (to make a <a href="mixed-fractions.html">mixed fraction</a>):</p>
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<h3 align="center">Answer = 2 <span class="intbl">
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<em>7</em>
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<strong>20</strong>
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</span></h3>
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</div>
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<div class="example">
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<h3>Example: Convert 0.333 to a fraction</h3>
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<p><b>Step 1:</b> Write down:</p>
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>0.333</em>
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<strong>1</strong>
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</span></p>
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</div>
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<p><b>Step 2:</b> Multiply both top and bottom by <b>1,000</b> (3 digits after the decimal point so that is 10×10×10=1,000)</p>
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>333</em>
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<strong>1000</strong>
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</span></p>
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</div>
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<p><b>Step 3:</b> Simplify Fraction:</p>
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<p class="center larger">Can't get any simpler!</p>
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<p> </p>
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<h3 align="center">Answer = <span class="intbl">
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<em>333</em>
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<strong>1000</strong>
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</span></h3>
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</div>
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<h2>But a Special Note:</h2>
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<p>If you really meant 0.333... (in other words 3s repeating forever which is called <i>3 recurring</i>) then we need to follow a special argument.
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In that case we write down:<br>
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<br></p>
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<div class="clear">
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<div class="clear">
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<p class="center larger"><span class="intbl">
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<em>0.333...</em>
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<strong>1</strong>
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</span></p>
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</div>
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</div>
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<p>Then multiply both top and bottom by 3:</p>
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<div class="clear">
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<table align="center" border="0" cellspacing="5" cellpadding="0" class="larger">
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<tr style="text-align:center;">
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<td colspan="3">× 3</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="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;" class="larger">
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<td><span class="intbl">
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<em>0.333...</em>
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<strong>1</strong>
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</span></td>
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<td style="width:30px;">=</td>
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<td><span class="intbl">
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<em>0.999...</em>
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<strong>3</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="30" width="79" ></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3">× 3</td>
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</tr>
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</table><br>
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</div>
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<p>And <b>0.999... = 1</b> (Does it? - see the <a href="9recurring.html">9 Recurring</a> discussion for more if you are interested), so:</p>
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<p class="center large">Answer = <span class="intbl">
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<em>1</em>
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<strong>3</strong>
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</span></p>
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<div class="fun">
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<h3>Conversion Tool</h3>
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<p>You can also try the <a href="converting-decimals-fractions-solver.html">Decimal to Fraction Calculator</a></p>
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</div>
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<p> </p>
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<div class="questions">944, 1358, 945, 1359, 3483, 3484, 3485, 3486, 946, 1360</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-solver.html">Decimal to Fraction Converter</a>
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<a href="converting-fractions-decimals.html">Converting Fractions to Decimals</a>
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<a href="converting-decimals-percents.html">Converting Decimals to Percents</a>
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<a href="fractions_multiplication.html">Multiplying Fractions</a>
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<a href="fractions_division.html">Dividing Fractions</a>
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<a href="simplifying-fractions.html">Simplifying Fractions</a>
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<a href="equivalent_fractions.html">Equivalent Fractions</a>
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<a href="decimals-menu.html">Decimals Index</a>
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