{"id":293,"date":"2023-02-15T16:23:47","date_gmt":"2023-02-15T16:23:47","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=293"},"modified":"2025-08-23T00:51:10","modified_gmt":"2025-08-23T00:51:10","slug":"whole-numbers-learn-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/whole-numbers-learn-it-1\/","title":{"raw":"Whole Numbers: Learn It 1","rendered":"Whole Numbers: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify whole numbers and counting numbers<\/li>\r\n\t<li>Write whole numbers in words<\/li>\r\n\t<li>Round whole numbers<\/li>\r\n\t<li>Add, subtract, multiply, and divide whole numbers<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Identify Counting Numbers and Whole Numbers<\/h2>\r\n<p>In elementary mathematics, we frequently use the most fundamental set of numbers, which we typically employ for counting objects: [latex]1, 2, 3, 4, 5, ...[\/latex] and so forth. These numbers are referred to as the <strong>counting numbers<\/strong>. The discovery of the number zero was a big step in the history of mathematics. Including zero with the counting numbers gives a new set of numbers called the <strong>whole numbers<\/strong>.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Whole and Counting Numbers<\/h3>\r\n<p><strong>Counting numbers<\/strong> start with [latex]1[\/latex] and continue.<\/p>\r\n<p>&nbsp;<\/p>\r\n<center>[latex]1,2,3,4,5\\dots[\/latex]<\/center>\r\n<p>&nbsp;<\/p>\r\n<strong>Whole numbers<\/strong> are the counting numbers and zero.\r\n\r\n<p>&nbsp;<\/p>\r\n<center>[latex]0,1,2,3,4,5\\dots[\/latex]<\/center><\/div>\r\n<\/section>\r\n<section class=\"textbox proTip\">The notation \u201c\u2026\u201d is called an ellipsis, which is another way to show \u201cand so on\u201d, or that the pattern continues endlessly.<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3165[\/ohm2_question]<\/section>\r\n<h3>Modeling Numbers and Number Lines<\/h3>\r\n<p>Counting numbers and whole numbers can be visualized on a number line, as shown below. The numbers on the number line increase from left to right, and decrease from right to left. The point labeled [latex]0[\/latex] is called the origin. The points are equally spaced to the right of [latex]0[\/latex] and labeled with the counting numbers.<\/p>\r\n<center>\r\n[caption id=\"attachment_296\" align=\"aligncenter\" width=\"750\"]<img class=\"wp-image-296 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line.png\" alt=\"An image of a number line from 0 to 6 in increments of one. An arrow above the number line pointing to the right with the label\" width=\"750\" height=\"121\" \/> Figure 1. A number line[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>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 [latex]537[\/latex] has a different value than the number [latex]735[\/latex]. Even though they use the same digits, their value is different because of the different placement of the [latex]3[\/latex],[latex]7[\/latex], and the [latex]5[\/latex].<\/p>\r\n<p>Base-[latex]10[\/latex] blocks provide a way to model place value. The blocks can be used to represent hundreds, tens, and ones. Notice in the image below that the tens rod is made up of [latex]10[\/latex] ones, and the hundreds square is made of [latex]10[\/latex] tens, or [latex]100[\/latex] ones.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"347\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215201\/CNX_BMath_Figure_01_01_004.png\" alt=\"An image with three items. The first item is a single block with the label &quot;A single block represents 1.&quot; The second item is a rod made up of 10 connected blocks with the label &quot;A rod represents 10.&quot; The third item is a square made up of 100 connected blocks with the label &quot;A square represents 100.&quot;\" width=\"347\" height=\"287\" \/> Figure 2. A block, rod, and square representing 1, 10, and 100, respectively[\/caption]\r\n<\/center>\r\n<section class=\"textbox example\">\r\n<p>The image below shows the number [latex]138[\/latex] modeled with base-[latex]10[\/latex]\u00a0blocks. We can use place value notation to show the value of the number [latex]138[\/latex].<\/p>\r\n<center><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215204\/CNX_BMath_Figure_01_01_005.png\" alt=\"An image consisting of three items. The first item is a square of 100 blocks, 10 blocks wide and 10 blocks tall, with the label \" width=\"431\" height=\"152\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n<center><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215205\/CNX_BMath_Figure_01_01_006_img.png\" alt=\"An image of the expression 100 + 30 + 8. The first digit of each number is highlighted and there is an arrow from each of them to the number 138.\" width=\"97\" height=\"93\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n<table id=\"fs-id1714120\" class=\"unnumbered\" 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.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Digit<\/th>\r\n<th>Place value<\/th>\r\n<th>Number<\/th>\r\n<th>Value<\/th>\r\n<th>Total value<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>hundreds<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]100[\/latex]<\/td>\r\n<td>[latex]100\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>tens<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]30\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>ones<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]+\\phantom{\\rule{.5 em}{0ex}}8\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]\\text{Sum =}138\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section>\r\n<section class=\"textbox example\">Use place value notation to find the value of the number modeled by the base-[latex]10[\/latex] blocks shown.<center><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215206\/CNX_BMath_Figure_01_01_007_img.png\" alt=\"An image consisting of three items. The first item is two squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is one horizontal rod containing 10 blocks. The third item is 5 individual blocks.\" \/><\/center><br \/>\r\n[reveal-answer q=\"664749\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"664749\"]<br \/>\r\nThere are [latex]2[\/latex] hundreds squares, which is [latex]200[\/latex].<br \/>\r\nThere is [latex]1[\/latex] tens rod, which is [latex]10[\/latex].<br \/>\r\nThere are [latex]5[\/latex] ones blocks, which is [latex]5[\/latex].<br \/>\r\n<center><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215208\/CNX_BMath_Figure_01_01_008_img.png\" alt=\"An image of the expression 200 + 10 + 5. The first digit of each number is highlighted and there is an arrow from each of them to the number 215.\" width=\"97\" height=\"89\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n<table id=\"fs-id1785447\" class=\"unnumbered\" 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.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Digit<\/th>\r\n<th>Place value<\/th>\r\n<th>Number<\/th>\r\n<th>Value<\/th>\r\n<th>Total value<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>hundreds<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]100[\/latex]<\/td>\r\n<td>[latex]200\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>tens<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]10\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>ones<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]+\\phantom{\\rule{.5 em}{0ex}}5\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]215\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>The base-[latex]10[\/latex] blocks model the number [latex]215[\/latex].<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\n<h3>Identify the Place Value of a Digit<\/h3>\r\n<p>By looking at base-[latex]10[\/latex]\u00a0blocks, we saw that each place in a number has a different value. A place value chart is a useful way to summarize this information. The place values are separated into groups of three, called <strong>periods<\/strong>. The periods are <em>ones, thousands, millions, billions, trillions<\/em>, and so on. In a written number, commas separate the periods.<\/p>\r\n<p>Just as with the base-[latex]10[\/latex] blocks, where the value of the tens rod is ten times the value of the ones block and the value of the hundreds square is ten times the tens rod, the value of each place in the place-value chart is ten times the value of the place to the right of it.<\/p>\r\n<section class=\"textbox example\">\r\n<p>The chart below\u00a0shows how the number [latex]5,278,194[\/latex] is written in a place value chart.<\/p>\r\n<center><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215214\/CNX_BMath_Figure_01_01_011.png\" alt=\"A chart titled 'Place Value' with fifteen columns and 4 rows, with the columns broken down into five groups of three. The header row shows Trillions, Billions, Millions, Thousands, and Ones. The next row has the values 'Hundred trillions', 'Ten trillions', 'trillions', 'hundred billions', 'ten billions', 'billions', 'hundred millions', 'ten millions', 'millions', 'hundred thousands', 'ten thousands', 'thousands', 'hundreds', 'tens', and 'ones'. The first 8 values in the next row are blank. Starting with the ninth column, the values are '5', '2', '7', '8', '1', '9', and '4'.\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n<ul id=\"fs-id930962\">\r\n\t<li>The digit [latex]5[\/latex] is in the millions place. Its value is [latex]5,000,000[\/latex].<\/li>\r\n\t<li>The digit [latex]2[\/latex] is in the hundred thousands place. Its value is [latex]200,000[\/latex].<\/li>\r\n\t<li>The digit [latex]7[\/latex] is in the ten thousands place. Its value is [latex]70,000[\/latex].<\/li>\r\n\t<li>The digit [latex]8[\/latex] is in the thousands place. Its value is [latex]8,000[\/latex].<\/li>\r\n\t<li>The digit [latex]1[\/latex] is in the hundreds place. Its value is [latex]100[\/latex].<\/li>\r\n\t<li>The digit [latex]9[\/latex] is in the tens place. Its value is [latex]90[\/latex].<\/li>\r\n\t<li>The digit [latex]4[\/latex] is in the ones place. Its value is [latex]4[\/latex].<\/li>\r\n<\/ul>\r\n<\/section>\r\n<ul id=\"fs-id930962\"><\/ul>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3166[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify whole numbers and counting numbers<\/li>\n<li>Write whole numbers in words<\/li>\n<li>Round whole numbers<\/li>\n<li>Add, subtract, multiply, and divide whole numbers<\/li>\n<\/ul>\n<\/section>\n<h2>Identify Counting Numbers and Whole Numbers<\/h2>\n<p>In elementary mathematics, we frequently use the most fundamental set of numbers, which we typically employ for counting objects: [latex]1, 2, 3, 4, 5, ...[\/latex] and so forth. These numbers are referred to as the <strong>counting numbers<\/strong>. The discovery of the number zero was a big step in the history of mathematics. Including zero with the counting numbers gives a new set of numbers called the <strong>whole numbers<\/strong>.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Whole and Counting Numbers<\/h3>\n<p><strong>Counting numbers<\/strong> start with [latex]1[\/latex] and continue.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]1,2,3,4,5\\dots[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Whole numbers<\/strong> are the counting numbers and zero.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]0,1,2,3,4,5\\dots[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox proTip\">The notation \u201c\u2026\u201d is called an ellipsis, which is another way to show \u201cand so on\u201d, or that the pattern continues endlessly.<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3165\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3165&theme=lumen&iframe_resize_id=ohm3165&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Modeling Numbers and Number Lines<\/h3>\n<p>Counting numbers and whole numbers can be visualized on a number line, as shown below. The numbers on the number line increase from left to right, and decrease from right to left. The point labeled [latex]0[\/latex] is called the origin. The points are equally spaced to the right of [latex]0[\/latex] and labeled with the counting numbers.<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_296\" aria-describedby=\"caption-attachment-296\" style=\"width: 750px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-296 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line.png\" alt=\"An image of a number line from 0 to 6 in increments of one. An arrow above the number line pointing to the right with the label\" width=\"750\" height=\"121\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line.png 750w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line-300x48.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line-65x10.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line-225x36.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/02\/15162536\/number-line-350x56.png 350w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><figcaption id=\"caption-attachment-296\" class=\"wp-caption-text\">Figure 1. A number line<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>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 [latex]537[\/latex] has a different value than the number [latex]735[\/latex]. Even though they use the same digits, their value is different because of the different placement of the [latex]3[\/latex],[latex]7[\/latex], and the [latex]5[\/latex].<\/p>\n<p>Base-[latex]10[\/latex] blocks provide a way to model place value. The blocks can be used to represent hundreds, tens, and ones. Notice in the image below that the tens rod is made up of [latex]10[\/latex] ones, and the hundreds square is made of [latex]10[\/latex] tens, or [latex]100[\/latex] ones.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 347px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215201\/CNX_BMath_Figure_01_01_004.png\" alt=\"An image with three items. The first item is a single block with the label &quot;A single block represents 1.&quot; The second item is a rod made up of 10 connected blocks with the label &quot;A rod represents 10.&quot; The third item is a square made up of 100 connected blocks with the label &quot;A square represents 100.&quot;\" width=\"347\" height=\"287\" \/><figcaption class=\"wp-caption-text\">Figure 2. A block, rod, and square representing 1, 10, and 100, respectively<\/figcaption><\/figure>\n<\/div>\n<section class=\"textbox example\">\n<p>The image below shows the number [latex]138[\/latex] modeled with base-[latex]10[\/latex]\u00a0blocks. We can use place value notation to show the value of the number [latex]138[\/latex].<\/p>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215204\/CNX_BMath_Figure_01_01_005.png\" alt=\"An image consisting of three items. The first item is a square of 100 blocks, 10 blocks wide and 10 blocks tall, with the label\" width=\"431\" height=\"152\" \/><\/div>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215205\/CNX_BMath_Figure_01_01_006_img.png\" alt=\"An image of the expression 100 + 30 + 8. The first digit of each number is highlighted and there is an arrow from each of them to the number 138.\" width=\"97\" height=\"93\" \/><\/div>\n<p>&nbsp;<\/p>\n<table id=\"fs-id1714120\" class=\"unnumbered\" 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.\">\n<thead>\n<tr valign=\"top\">\n<th>Digit<\/th>\n<th>Place value<\/th>\n<th>Number<\/th>\n<th>Value<\/th>\n<th>Total value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]1[\/latex]<\/td>\n<td>hundreds<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]100[\/latex]<\/td>\n<td>[latex]100\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]3[\/latex]<\/td>\n<td>tens<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]30\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]8[\/latex]<\/td>\n<td>ones<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]+\\phantom{\\rule{.5 em}{0ex}}8\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>[latex]\\text{Sum =}138\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section class=\"textbox example\">Use place value notation to find the value of the number modeled by the base-[latex]10[\/latex] blocks shown.<\/p>\n<div style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215206\/CNX_BMath_Figure_01_01_007_img.png\" alt=\"An image consisting of three items. The first item is two squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is one horizontal rod containing 10 blocks. The third item is 5 individual blocks.\" \/><\/div>\n<div class=\"wp-nocaption \"><\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q664749\">Show Solution<\/button><\/p>\n<div id=\"q664749\" class=\"hidden-answer\" style=\"display: none\">\nThere are [latex]2[\/latex] hundreds squares, which is [latex]200[\/latex].<br \/>\nThere is [latex]1[\/latex] tens rod, which is [latex]10[\/latex].<br \/>\nThere are [latex]5[\/latex] ones blocks, which is [latex]5[\/latex].<\/p>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215208\/CNX_BMath_Figure_01_01_008_img.png\" alt=\"An image of the expression 200 + 10 + 5. The first digit of each number is highlighted and there is an arrow from each of them to the number 215.\" width=\"97\" height=\"89\" \/><\/div>\n<p>&nbsp;<\/p>\n<table id=\"fs-id1785447\" class=\"unnumbered\" 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.\">\n<thead>\n<tr valign=\"top\">\n<th>Digit<\/th>\n<th>Place value<\/th>\n<th>Number<\/th>\n<th>Value<\/th>\n<th>Total value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]2[\/latex]<\/td>\n<td>hundreds<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]100[\/latex]<\/td>\n<td>[latex]200\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]1[\/latex]<\/td>\n<td>tens<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]10\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]5[\/latex]<\/td>\n<td>ones<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]+\\phantom{\\rule{.5 em}{0ex}}5\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>[latex]215\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>The base-[latex]10[\/latex] blocks model the number [latex]215[\/latex].\n<\/div>\n<\/div>\n<\/section>\n<h3>Identify the Place Value of a Digit<\/h3>\n<p>By looking at base-[latex]10[\/latex]\u00a0blocks, we saw that each place in a number has a different value. A place value chart is a useful way to summarize this information. The place values are separated into groups of three, called <strong>periods<\/strong>. The periods are <em>ones, thousands, millions, billions, trillions<\/em>, and so on. In a written number, commas separate the periods.<\/p>\n<p>Just as with the base-[latex]10[\/latex] blocks, where the value of the tens rod is ten times the value of the ones block and the value of the hundreds square is ten times the tens rod, the value of each place in the place-value chart is ten times the value of the place to the right of it.<\/p>\n<section class=\"textbox example\">\n<p>The chart below\u00a0shows how the number [latex]5,278,194[\/latex] is written in a place value chart.<\/p>\n<div style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215214\/CNX_BMath_Figure_01_01_011.png\" alt=\"A chart titled 'Place Value' with fifteen columns and 4 rows, with the columns broken down into five groups of three. The header row shows Trillions, Billions, Millions, Thousands, and Ones. The next row has the values 'Hundred trillions', 'Ten trillions', 'trillions', 'hundred billions', 'ten billions', 'billions', 'hundred millions', 'ten millions', 'millions', 'hundred thousands', 'ten thousands', 'thousands', 'hundreds', 'tens', and 'ones'. The first 8 values in the next row are blank. Starting with the ninth column, the values are '5', '2', '7', '8', '1', '9', and '4'.\" \/><\/div>\n<p>&nbsp;<\/p>\n<ul id=\"fs-id930962\">\n<li>The digit [latex]5[\/latex] is in the millions place. Its value is [latex]5,000,000[\/latex].<\/li>\n<li>The digit [latex]2[\/latex] is in the hundred thousands place. Its value is [latex]200,000[\/latex].<\/li>\n<li>The digit [latex]7[\/latex] is in the ten thousands place. Its value is [latex]70,000[\/latex].<\/li>\n<li>The digit [latex]8[\/latex] is in the thousands place. Its value is [latex]8,000[\/latex].<\/li>\n<li>The digit [latex]1[\/latex] is in the hundreds place. Its value is [latex]100[\/latex].<\/li>\n<li>The digit [latex]9[\/latex] is in the tens place. Its value is [latex]90[\/latex].<\/li>\n<li>The digit [latex]4[\/latex] is in the ones place. Its value is [latex]4[\/latex].<\/li>\n<\/ul>\n<\/section>\n<ul><\/ul>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3166\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3166&theme=lumen&iframe_resize_id=ohm3166&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"Lynn Marecek & MaryAnne Anthony-Smith\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-1-introduction-to-whole-numbers\",\"project\":\"1.1 Introduction to Whole Numbers\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":290,"module-header":"learn_it","content_attributions":[{"type":"original","description":"Revision and Adaptation","author":"","organization":"Lumen Learning","url":"","project":"","license":"cc-by","license_terms":""},{"type":"cc-attribution","description":"Prealgebra","author":"Lynn Marecek & MaryAnne Anthony-Smith","organization":"OpenStax","url":"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-1-introduction-to-whole-numbers","project":"1.1 Introduction to Whole Numbers","license":"cc-by","license_terms":"Access for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757"}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/293"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":63,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/293\/revisions"}],"predecessor-version":[{"id":15570,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/293\/revisions\/15570"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/290"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/293\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=293"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=293"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=293"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}