<p>In&nbsp;2013,2013,&nbsp;the U.S. Census Bureau reported the population of the state of New York as&nbsp;19,651,12719,651,127&nbsp;people. It might be enough to say that the population is approximately&nbsp;2020&nbsp;million. The word&nbsp;<em>approximately</em>&nbsp;means that&nbsp;2020&nbsp;million is not the exact population, but is close to the exact value.</p>

<p>The process of approximating a number is called&nbsp;rounding. Numbers are rounded to a specific place value depending on how much accuracy is needed.&nbsp;2020&nbsp;million was achieved by rounding to the millions place. Had we rounded to the one hundred thousands place, we would have&nbsp;19,700,00019,700,000&nbsp;as a result. Had we rounded to the ten thousands place, we would have&nbsp;19,650,00019,650,000&nbsp;as a result, and so on. The place value to which we round to depends on how we need to use the number.</p>

<p>Using the number line can help you visualize and understand the rounding process. Look at the number line in&nbsp;<a href="https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers#CNX_BMath_Figure_01_01_019">Figure 1.7</a>. Suppose we want to round the number&nbsp;7676&nbsp;to the nearest ten. Is&nbsp;7676&nbsp;closer to&nbsp;7070&nbsp;or&nbsp;8080&nbsp;on the number line?</p>

<p><img alt="An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is an orange dot at the value “76” on the number line." src="https://openstax.org/resources/37b6df2651510551d9071da3f6b8eb0719ff6633" /></p>

<p>Figure&nbsp;1.7&nbsp;We can see that&nbsp;7676&nbsp;is closer to&nbsp;8080&nbsp;than to&nbsp;70.70.&nbsp;So&nbsp;7676&nbsp;rounded to the nearest ten is&nbsp;80.80.</p>

<p>Now consider the number&nbsp;72.72.&nbsp;Find&nbsp;7272&nbsp;in&nbsp;<a href="https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers#CNX_BMath_Figure_01_01_020">Figure 1.8</a>.</p>

<p><img alt="An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is an orange dot at the value “72” on the number line." src="https://openstax.org/resources/e67bcef2dedda9aa2d1306e9ee1a994ccd86e8c1" /></p>

<p>Figure&nbsp;1.8&nbsp;We can see that&nbsp;7272&nbsp;is closer to&nbsp;70,70,&nbsp;so&nbsp;7272&nbsp;rounded to the nearest ten is&nbsp;70.70.</p>

<p>How do we round&nbsp;7575&nbsp;to the nearest ten. Find&nbsp;7575&nbsp;in&nbsp;<a href="https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers#CNX_BMath_Figure_01_01_021">Figure 1.9</a>.</p>

<p><img alt="An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is an orange dot at the value “75” on the number line." src="https://openstax.org/resources/50e1604fc69fede5e2888928a5010a8a5c196bef" /></p>

<p>Figure&nbsp;1.9&nbsp;The number&nbsp;7575&nbsp;is exactly midway between&nbsp;7070&nbsp;and&nbsp;80.80.</p>

<p>So that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number,&nbsp;80.80.&nbsp;So,&nbsp;7575&nbsp;rounded to the nearest ten is&nbsp;80.80.</p>

<p>Now that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than&nbsp;5,5,&nbsp;round down. If it is greater than or equal to&nbsp;5,5,&nbsp;round up.</p>

<p>So, for example, to round&nbsp;7676&nbsp;to the nearest ten, we look at the digit in the ones place.</p>

<p><img alt="An image of value “76”. The text “tens place” is in blue and points to number 7 in “76”. The text “is greater than 5” is in red and points to the number 6 in “76”." src="https://openstax.org/resources/ac59753452bda33d47b5a9b6323a5b6eb970a9f8" /></p>

<p>&nbsp;</p>

<p>The digit in the ones place is a&nbsp;6.6.&nbsp;Because&nbsp;66&nbsp;is greater than or equal to&nbsp;5,5,&nbsp;we increase the digit in the tens place by one. So the&nbsp;77&nbsp;in the tens place becomes an&nbsp;8.8.&nbsp;Now, replace any digits to the right of the&nbsp;88&nbsp;with zeros. So,&nbsp;7676&nbsp;rounds to&nbsp;80.</p>

<p><img alt="An image of the value “76”. The “6” in “76” is crossed out and has an arrow pointing to it which says “replace with 0”. The “7” has an arrow pointing to it that says “add 1”. Under the value “76” is the value “80”." src="https://openstax.org/resources/43d39fbc30343be3e28fa19af0fa1cbada0db25e" /></p>

<p>Let&rsquo;s look again at&nbsp;rounding&nbsp;7272&nbsp;to the nearest&nbsp;10.10.&nbsp;Again, we look to the ones place.</p>

<p><img alt="An image of value “72”. The text “tens place” is in blue and points to number 7 in “72”. The text “is less than 5” is in red and points to the number 2 in “72”." src="https://openstax.org/resources/4d8896d3e6d604c3bc4c456640e4b400f03a24b8" /></p>

<p>The digit in the ones place is&nbsp;2.2.&nbsp;Because&nbsp;22&nbsp;is less than&nbsp;5,5,&nbsp;we keep the digit in the tens place the same and replace the digits to the right of it with zero. So&nbsp;7272&nbsp;rounded to the nearest ten is&nbsp;70.</p>

<p><img alt="An image of the value “72”. The “2” in “72” is crossed out and has an arrow pointing to it which says “replace with 0”. The “7” has an arrow pointing to it that says “do not add 1”. Under the value “72” is the value “70”." src="https://openstax.org/resources/739ab4ea290fbf12281c63f83068ce837625e531" /></p>

<p>HOW TO</p>

<p>Round a whole number to a specific place value.</p>

<ol style="list-style-type:decimal">
	<li>Step 1. Locate the given place value. All digits to the left of that place value do not change unless the digit immediately to the left is 9, in which case it may. (See Step 3.)</li>
	<li>Step 2. Underline the digit to the right of the given place value.</li>
	<li>Step 3. Determine if this digit is greater than or equal to&nbsp;5.5.
	<ul>
		<li>Yes&mdash;add&nbsp;11&nbsp;to the digit in the given place value. If that digit is 9, replace it with 0 and add 1 to the digit immediately to its left. If that digit is also a 9, repeat.</li>
		<li>No&mdash;do not change the digit in the given place value.</li>
	</ul>
	</li>
	<li>Step 4. Replace all digits to the right of the given place value with zeros.</li>
</ol>

<p><strong>EXAMPLE&nbsp;1.8</strong>&nbsp;Round&nbsp;843843&nbsp;to the nearest ten.</p>

<p><strong>Solution</strong></p>

<p><br />
&nbsp;&nbsp;<a href="https://openstax.org">Access for free at https://openstax.org.</a></p>