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<center>
<h1>Ordering Decimals</h1> </center>
<p class="center"><i>&quot;Could I have a 3.65 and an 0.8, please ... ?&quot; <br />
NO, not THAT type of ordering. I mean <b>putting them in order</b> ...</i></p>
<p>Ordering <a href="decimals.html">decimals</a> can be tricky. Because often we look at 0.42 and 0.402 and say that 0.402 must be bigger because there are more digits. But no! </p>
<p>We can use this method to see which decimals are bigger:&nbsp; </p>
<ul>
<li>Set up a table with the <b>decimal point in the same place</b> for each number.</li>
<li>Put in each number.</li>
<li>Fill in the <b>empty squares with zeros</b>.</li>
<li>Compare using the <b>first column</b> on the left</li>
<li>If the digits are equal move to the <b>next column</b> to the right until one number wins.</li>
</ul>
<table border="0" align="center">
<tr>
<td>
<p class="Larger">If you want <b>ascending</b> order you always pick the smallest first</p>
</td>
<td width="10">&nbsp;</td>
<td><img src="geometry/images/slope-pos.svg" alt="ascend" /></td>
</tr>
<tr>
<td><span class="Larger">If you want <b>descending</b> order you always pick the largest first</span></td>
<td>&nbsp;</td>
<td><img src="geometry/images/slope-neg.svg" alt="descend" /></td>
</tr>
</table>
<h2>Example: Put the following decimals in ascending order:</h2>
<p align="center"><font face="Courier New, Courier, mono" size="+1">1.506,
1.56, 0.8</font></p>
<p>In a table they look like this:</p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%"> Ones </td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">0</td>
<td class="larger">6</td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">6</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">8</td>
<td class="larger">&nbsp;</td>
<td class="larger">&nbsp;</td>
</tr>
</table>
<h3> Fill in the empty squares with zeros:</h3>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">0</td>
<td class="larger">6</td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">6</td>
<td class="larger"><span class="hi">0</span></td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">8</td>
<td class="larger"><span class="hi">0</span></td>
<td class="larger"><span class="hi">0</span></td>
</tr>
</table>
<h3>Compare using the first column (Ones)</h3>
<p>Two of them are &quot;1&quot;s and the other is a &quot;0&quot;. Ascending order needs smallest first, and so &quot;0&quot; is the winner:</p>
<p class="center large">Answer so far: <b>0.8</b></p>
<p>Now we can remove 0.8 from the list:</p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">0</td>
<td class="larger">6</td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">6</td>
<td class="larger">0</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">.</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
</table>
<h3>Compare the Tenths</h3>
<p>Now there are two numbers with the same &quot;Tenths&quot; value of 5, so move along to the &quot;Hundredths&quot; for the tie-breaker </p>
<h3>Compare the Hundredths</h3>
<p>One of those has a 6 in the hundredths, and the other has a 0, so the 0 wins (remember we are looking for the smallest each time). In other words 1.506 is less than 1.56:</p>
<p align="center" class="large">Answer so far: <b>0.8, 1.506</b></p>
<p>Remove 1.506 from the list:</p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">.</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">5</td>
<td class="larger">6</td>
<td class="larger">0</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">.</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
</table>
<p>Only one number left, it must be the largest:</p>
<p align="center" class="large">Answer: <b>0.8, 1.506, 1.56</b></p>
<p>Done! </p>
<h2>Example: Put the following decimals in DESCENDING order:</h2>
<p align="center"><font face="Courier New, Courier, mono" size="+1">0.402,
0.42, 0.375, 1.2, 0.85</font> </p>
<p>In a table they look like this:</p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">0</td>
<td class="larger">2</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">2</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">3</td>
<td class="larger">7</td>
<td class="larger">5</td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">2</td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">8</td>
<td class="larger">5</td>
<td>&nbsp;</td>
</tr>
</table>
<p>And we want to go from <b>highest to lowest</b> (descending).</p>
<h3> Fill in the empty squares with zeros:</h3>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">0</td>
<td class="larger">2</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">2</td>
<td class="larger"><span class="hi">0</span></td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">3</td>
<td class="larger">7</td>
<td class="larger">5</td>
</tr>
<tr align="center">
<td class="larger">1</td>
<td class="larger">.</td>
<td class="larger">2</td>
<td class="larger"><span class="hi">0</span></td>
<td class="larger"><span class="hi">0</span></td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">8</td>
<td class="larger">5</td>
<td class="larger"><span class="hi">0</span></td>
</tr>
</table>
<h3>Compare using the first column (Ones):</h3>
<p>There is a 1, all the rest are 0. Descending order needs largest first, so 1.2 must be the highest. (Write it down in your answer and cross it off the table).</p>
<p align="center" class="large">Answer so far: <b>1.2</b></p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">0</td>
<td class="larger">2</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">2</td>
<td class="larger">0</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">3</td>
<td class="larger">7</td>
<td class="larger">5</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">8</td>
<td class="larger">5</td>
<td class="larger">0</td>
</tr>
</table>
<h3>Compare the Tenths.</h3>
<p><span class="beach">The 8 is highest, so 0.85 is next in value.</span></p>
<p align="center" class="large">Answer so far: <b>1.2, 0.85</b></p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">0</td>
<td class="larger">2</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">4</td>
<td class="larger">2</td>
<td class="larger">0</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">3</td>
<td class="larger">7</td>
<td class="larger">5</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
</table>
<p>Now there are two numbers with the same &quot;Tenths&quot; value of 4, so move along to the &quot;Hundredths&quot; for the tie-breaker </p>
<p>One number has a 2 in the hundredths, and the other has a 0, so the 2 wins. So 0.42 is bigger than 0.402:</p>
<p align="center" class="large">Answer so far: <b>1.2, 0.85, 0.42, 0.402</b></p>
<table width="420" border="1" align="center">
<tr align="center">
<td width="22%">Ones</td>
<td width="10%"> Decimal
<br /> Point </td>
<td width="22%"> Tenths </td>
<td width="22%"> Hundredths </td>
<td width="22%"> Thousandths </td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
<tr align="center">
<td class="larger">0</td>
<td class="larger">.</td>
<td class="larger">3</td>
<td class="larger">7</td>
<td class="larger">5</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
<tr align="center">
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
<td class="larger">-</td>
</tr>
</table>
<p>Only 0.375 left, so the answer is:</p>
<p align="center" class="large"><b>Answer: 1.2, 0.85, 0.42, 0.402, 0.375</b></p>
<p>&nbsp;</p>
<div class="beach"></div>
<div class="center80">
<h3>Game</h3>
<p>Now, go practice with this special <a href="numbers/ordering-gamefbb9.html?m=Dec-Tricky">Decimal Ordering Game</a> ! </p>
</div>
<div class="questions">
<script type="text/javascript">
getQ(5905, 5906, 5907, 5908, 956, 957, 1334, 1335, 3593, 3594);
</script>&nbsp; </div>
<div class="related"> <a href="ordering-numbers.html">Ordering Numbers</a> <a href="numbers/ordering-game.html">Ordering Games</a> <a href="rounding-numbers.html">Rounding Numbers</a> <a href="numbers/index.html">Numbers Index</a></div>
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