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<title>Rounding Numbers</title>
<meta name="description" content="Learn that rounding means making a number simpler but keeping its value close to what it was, with examples." />
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<h1 align="center">Rounding Numbers</h1>
<h2>What is &quot;Rounding&quot; ?</h2>
<p>Rounding means making a number <b>simpler</b> but keeping its value close to what it was. </p>
<p><i> The result is less accurate, but easier to use. </i></p>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="numbers/images/round-70s.svg" alt="round 73 is 70, 76 is 80" /></p>
<p>Example: <b>73</b> rounded to the nearest ten is <b>70</b>, because 73 is closer to 70 than to 80. But 76 goes <b>up</b> to 80.</p>
</div>
<h2>Common Method</h2>
<p>There are <a href="numbers/rounding-methods.html">several different methods for rounding</a>. Here we look at the <b>common method</b>, the one used by most people.</p>
<p>First some examples (explanations follow):</p>
<script type="text/javascript">playerMain("numbers/images/round-tens.txt",360,210,"");</script><p>&nbsp;</p>
<script type="text/javascript">playerMain("numbers/images/round-hundredths.txt",360,210,"");</script>
<h2>How to Round Numbers</h2>
<ul>
<li>Decide which is the last digit to <b>keep</b></li>
<li>Leave it the same if the <b>next digit</b> is less than 5 (this is called <i>rounding down</i>)</li>
<li>But increase it by 1 if the next digit is 5 or more (this is called <i>rounding up</i>)</li>
</ul>
<div class="example">
<h3>Example: Round 74 to the nearest 10 </h3>
<ul>
<li>We want to keep the &quot;7&quot; (it is in the 10s position)</li>
<li>The next digit is &quot;4&quot; which is less than 5, so no change is needed to &quot;7&quot;</li>
</ul>
<p><b>Answer: 70 </b></p>
<p>(74 gets &quot;rounded down&quot;)</p>
</div>
<div class="example">
<h3>Example: Round 86 to the nearest 10 </h3>
<ul>
<li>We want to keep the &quot;8&quot;</li>
<li>The next digit is &quot;6&quot; which is 5 or more, so increase the &quot;8&quot; by 1 to &quot;9&quot;</li>
</ul>
<p><b>Answer: 90 </b></p>
<p>(86 gets &quot;rounded up&quot;)</p>
</div>
<p>So: when the first digit <b>removed</b> is 5 or more, increase the last digit <b>remaining</b> by 1.</p>
<h2>Why does 5 go up ?</h2>
<p>5 is in the middle ... so we <b>could</b> go up or down. But we need a method that everyone agrees to.</p>
<p align="center">So think about sport: we should have the same number of players on each team, right?</p>
<table border="0" align="center">
<tr>
<td><img src="images/soccer-teams.jpg" width="209" height="86" alt="soccer teams" /></td>
<td><ul>
<li>0,1,2,3 and 4 are on team &quot;down&quot;</li>
<li>5,6,7,8 and 9 are on team &quot;up&quot;</li>
</ul></td>
</tr>
</table>
<p><i>And that is the &quot;common&quot; method of rounding. </i>Read about <a href="numbers/rounding-methods.html">other methods of rounding</a>.</p>
<p class="fun">A farmer counted 87 cows in the field, but when he rounded them up he had 90.</p>
<h2>Rounding Decimals</h2>
<p>First work out which number will be left when we finish.</p>
<ul>
<li>Rounding to <b>tenths</b> means to leave <b>one number</b> after the decimal point.</li>
<li>Rounding to <b>hundredths</b> means to leave <b>two numbers</b> after the decimal point.</li>
<li>etc.</li>
</ul>
<div class="example">
<h3>3.1416 rounded to hundredths is 3.14<br />
</h3>
<p class="center">as the next digit (1) is less than 5</p>
</div>
<div class="example">
<h3>3.1416 rounded to thousandths is 3.142<br />
</h3>
<p class="center">as the next digit (6) is more than 5</p>
</div>
<div class="example">
<h3>1.2735 rounded to tenths is 1.3</h3>
<p class="center">as the next digit (7) is 5 or more</p>
</div>
<p>To round to &quot;so many decimal places&quot; count that many digits from the decimal point:</p>
<div class="example">
<h3>1.2735 rounded to 3 decimal places is 1.274</h3>
<p class="center">as the next digit (5) is 5 or more</p>
</div>
<h2>Rounding Whole Numbers</h2>
<p>We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero.</p>
<div class="example">
<h3>134.9 rounded to tens is 130</h3>
<p class="center">as the next digit (4) is less than 5</p>
</div>
<div class="example">
<h3>12,690 rounded to thousands is 13,000</h3>
<p class="center">as the next digit (6) is 5 or more</p>
</div>
<div class="example">
<h3>15.239 rounded to ones is 15</h3>
<p class="center">as the next digit (2) is less than 5</p>
</div>
<h2>Rounding to Significant Digits</h2>
<p>To round to &quot;so many&quot; significant digits, <b>count digits from left to right</b>, and then round off from there. </p>
<div class="example">
<h3>1.239 rounded to 3 significant digits is 1.24</h3>
<p class="center">as the next digit (9) is 5 or more</p>
</div>
<div class="example">
<h3>134.9 rounded to 1 significant digit is 100</h3>
<p class="center">as the next digit (3) is less than 5</p>
</div>
<p>When there are leading zeros (such as 0.006), don't count them because they are only there to show how small the number is:</p>
<div class="example">
<h3>0.0165 rounded to 2 significant digits is 0.017</h3>
<p class="center">as the next digit (5) is 5 or more</p>
</div>
<p class="center"><img src="numbers/images/significant-digits.svg" alt="significant digits" /></p>
<h2>Significant Digit Calculator</h2>
<script type="text/javascript">roundsigMain();</script>
<p>(Try increasing or decreasing the number of significant digits. Also try numbers with lots of zeros in front of them like 0.00314, 0.0000314 etc)</p>
<p>&nbsp;</p>
<div class="questions">
<script type="text/javascript">getQ(951,952,953,954,955,1329,1330,1331, 3481, 3482);</script>&nbsp; </div>
<div class="related"> <a href="decimals.html">Decimals</a> <a href="decimals-menu.html">Decimals Index</a> <a href="numbers/number-line-zoom.html">Zoomable Number Line</a> <a href="numbers/rounding-methods.html">Rounding Methods</a> <a href="numbers/rounding-tool.html">Rounding Tool</a> <a href="index-notation-powers.html">Powers of 10</a> <a href="metric-numbers.html">Metric Numbers</a> <a href="converting-decimals-fractions.html">Convert Decimals to Fractions</a> <a href="converting-fractions-decimals.html">Converting Fractions to Decimals</a></div>
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