<h2 data-type="title">Model Whole Numbers</h2>
<p id="fs-id1862565">Our number system is called a <strong>place value system</strong> because the value of a digit depends on its position, or place, in a number. The number $537$ has a different value than the number $735$. Even though they use the same digits, their value is different because of the different placement of the $3$ and the $7$ and the $5$.</p>
<p id="fs-id1461000">Money gives us a familiar model of place value. Suppose a wallet contains three $$100$ bills, seven $$10$ bills, and four $$1$ bills. The amounts are summarized in the figure below. How much money is in the wallet?</p>
<div class="wp-caption alignnone" id="attachment_99284" style="width: 597px"><a href="https://data.ulearngo.com/assets/9a00733a-5718-46a5-b87f-ed70efe21005"><img alt="dollar-bills" class="size-full wp-image-99284" height="219" src="https://data.ulearngo.com/assets/9a00733a-5718-46a5-b87f-ed70efe21005" width="597"/></a><p class="wp-caption-text">Image credit: OpenStax Prealgebra</p></div>
<figure id="CNX_BMath_Figure_01_01_002"></figure>
<p id="fs-id2243766">Find the total value of each kind of bill, and then add to find the total. The wallet contains $$374$.</p>
<p><a href="https://data.ulearngo.com/assets/451935ee-14d2-4bf7-9ff5-0b64f45b2c49"><img alt="total-bills" class="size-full wp-image-99285" height="90" src="https://data.ulearngo.com/assets/451935ee-14d2-4bf7-9ff5-0b64f45b2c49" width="126"/></a></p>
<p id="fs-id865961">Base-10 blocks provide another way to model place value, as shown in the figure below. The blocks can be used to represent hundreds, tens, and ones. Notice that the tens rod is made up of $10$ ones, and the hundreds square is made of $10$ tens, or $100$ ones.</p>
<div class="wp-caption alignnone" id="attachment_99286" style="width: 347px"><a href="https://data.ulearngo.com/assets/45592bf6-09bf-4e30-b4a3-1cf410226afa"><img alt="base-10 blocks" class="size-full wp-image-99286" height="287" src="https://data.ulearngo.com/assets/45592bf6-09bf-4e30-b4a3-1cf410226afa" width="347"/></a><p class="wp-caption-text">Image credit: OpenStax Prealgebra</p></div>
<figure id="CNX_BMath_Figure_01_01_004"></figure>
<p id="fs-id2860981">The figure below shows the number $138$ modeled with $\text{base}$-$10$ blocks.</p>
<div class="wp-caption alignnone" id="attachment_99287" style="width: 431px"><a href="https://data.ulearngo.com/assets/1322c91e-2a8e-454d-8a5a-abc49c1828a0"><img alt="base-10-blocks-2" class="size-full wp-image-99287" height="152" src="https://data.ulearngo.com/assets/1322c91e-2a8e-454d-8a5a-abc49c1828a0" width="431"/></a><p class="wp-caption-text">We use place value notation to show the value of the number $138$. Image credit: OpenStax Prealgebra</p></div>
<p><a href="https://data.ulearngo.com/assets/20e77a58-c363-4a65-b124-65be01eb3ae7"><img alt="number-138" class="size-full wp-image-99288 alignnone" height="93" src="https://data.ulearngo.com/assets/20e77a58-c363-4a65-b124-65be01eb3ae7" width="97"/></a></p>
<table class="unnumbered" data-label="" id="fs-id1714120" summary="This is a table with 3 columns and 5 rows. The first row is a header row. Each column in this row is labeled: first column is labeled Place value, the second column is labeled Digit, and the third column is labeled total value. Under the heading Place value in the second row it states hundreds, below that it states tens, and below that it states ones. In the next column under Digit, there is a 1 in the second row, a 3 in the third row, and an 8 in the fourth row. In the next column under Total value it has 100 in the second row, 30 in the third row, 8 in the fourth row and the number 138 in the fifth row.">
<thead>
<tr valign="top">
<th data-align="center" scope="col">Digit</th>
<th data-align="center" scope="col">Place value</th>
<th data-align="center" scope="col">Number</th>
<th data-align="center" scope="col">Value</th>
<th data-align="right" scope="col">Total value</th>
</tr>
</thead>
<tbody>
<tr valign="top">
<td data-align="center">$1$</td>
<td data-align="center">hundreds</td>
<td data-align="center">$1$</td>
<td data-align="center">$100$</td>
<td data-align="right">$100$</td>
</tr>
<tr valign="top">
<td data-align="center">$3$</td>
<td data-align="center">tens</td>
<td data-align="center">$3$</td>
<td data-align="center">$10$</td>
<td data-align="right">$30$</td>
</tr>
<tr valign="top">
<td data-align="center">$8$</td>
<td data-align="center">ones</td>
<td data-align="center">$8$</td>
<td data-align="center">$1$</td>
<td data-align="right">$8$</td>
</tr>
<tr valign="top">
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td data-align="right">$\text{Sum} = 138$</td>
</tr>
</tbody>
</table>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p id="fs-id2939641">Use place value notation to find the value of the number modeled by the $\text{base}$-$10$ blocks shown.</p>
<div class="wp-caption alignnone" id="attachment_99293" style="width: 556px"><a href="https://data.ulearngo.com/assets/0790d687-1144-4592-8de8-c90a91da899b"><img alt="" class="wp-image-99293 size-full" height="177" src="https://data.ulearngo.com/assets/0790d687-1144-4592-8de8-c90a91da899b" width="556"/></a><p class="wp-caption-text">Image credit: OpenStax Prealgebra</p></div>
<h4 data-type="title">Solution</h4>
<p id="fs-id1249764">There are $2$ hundreds squares, which is $200.$</p>
<p id="fs-id1348273">There is $1$ tens rod, which is $10.$</p>
<p id="fs-id3302675">There are $5$ ones blocks, which is $5.$</p>
<p><a href="https://data.ulearngo.com/assets/b6ba842b-62f5-45a9-ad89-2ccefb2149f1"><img alt="number-215" class="size-full wp-image-99294 alignnone" height="89" src="https://data.ulearngo.com/assets/b6ba842b-62f5-45a9-ad89-2ccefb2149f1" width="97"/></a></p>
<table class="unnumbered" data-label="" id="fs-id1785447" summary="This is a table with 3 columns and 5 rows. The first row is a header row. Each column in this row is labeled: first column is labeled Place value,  the second column is labeled Digit, and the third column is labeled total value. Under the heading Place value in the second row it states hundreds, below that it states tens, and below that it states ones. In the next column under Digit, there is a 2 in the second row, a 1 in the third row, and an 5 in the fourth row. In the next column under Total value it has 200 in the second row, 10 in the third row, 5 in the fourth row and the number 215 in the fifth row.">
<thead>
<tr valign="top">
<th data-align="center" scope="col">Digit</th>
<th data-align="center" scope="col">Place value</th>
<th data-align="center" scope="col">Number</th>
<th data-align="center" scope="col">Value</th>
<th data-align="right" scope="col">Total value</th>
</tr>
</thead>
<tbody>
<tr valign="top">
<td data-align="center">$2$</td>
<td data-align="center">hundreds</td>
<td data-align="center">$2$</td>
<td data-align="center">$100$</td>
<td data-align="right">$200$</td>
</tr>
<tr valign="top">
<td data-align="center">$1$</td>
<td data-align="center">tens</td>
<td data-align="center">$1$</td>
<td data-align="center">$10$</td>
<td data-align="right">$10$</td>
</tr>
<tr valign="top">
<td data-align="center">$5$</td>
<td data-align="center">ones</td>
<td data-align="center">$5$</td>
<td data-align="center">$1$</td>
<td data-align="right">$5$</td>
</tr>
<tr valign="top">
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td data-align="right">$\text{Sum} = 215$</td>
</tr>
</tbody>
</table>
<p id="fs-id1381620">The $\text{base}$-$10$ blocks model the number $215.$</p>
</div>
</div>
<h2>Video: Writing a Whole Number in Digits from Words</h2>
<p><em>We'll talk more about this in the next lesson. Video credit: <a href="http://www.mathispower4u.yolasite.com">Mathispower4u</a></em></p>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="480" src="https://www.youtube.com/embed/H9HpkvY_iaE?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="640"></iframe></p>

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Model Whole Numbers

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Explore the world of numbers and learn about their history, properties, and applications, including place value, addition, subtraction, multiplication, and division.


Model Whole Numbers

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