{"id":4591,"date":"2020-04-21T00:19:04","date_gmt":"2020-04-21T00:19:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/whole-numbers-and-place-value\/"},"modified":"2024-06-26T17:38:16","modified_gmt":"2024-06-26T17:38:16","slug":"whole-numbers-and-place-value","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/whole-numbers-and-place-value\/","title":{"raw":"Whole Numbers and Place Value","rendered":"Whole Numbers and Place Value"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify the whole numbers from a list of numbers<\/li>\r\n \t<li>Identify the counting numbers from a list of numbers<\/li>\r\n \t<li>Use place value notation to find the place value of a number modeled by base-10 blocks<\/li>\r\n \t<li>Identify the place value of a digit in a number<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h2>Identify Counting Numbers and Whole Numbers<\/h2>\r\nLearning algebra is similar to learning a language. You start with a basic vocabulary and then add to it as you go along. You need to practice often until the vocabulary becomes easy to you. The more you use the vocabulary, the more familiar it becomes.\r\n\r\nAlgebra uses numbers and symbols to represent words and ideas. Let\u2019s look at the numbers first. The most basic numbers used in algebra are those we use to count objects: [latex]1,2,3,4,5,\\dots [\/latex] and so on. These are called the counting numbers. The notation \"\u2026\" is called an ellipsis, which is another way to show \"and so on\", or that the pattern continues endlessly. Counting numbers are also called natural numbers.\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Counting Numbers or Natural Numbers<\/h3>\r\nThe counting numbers start with [latex]1[\/latex] and continue.\r\n[latex]1,2,3,4,5\\dots[\/latex]\r\n\r\n<\/div>\r\nCounting numbers and whole numbers can be visualized on a number line as shown below.\r\n\r\nThe numbers on the number line increase from left to right, and decrease from right to left.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215156\/CNX_BMath_Figure_01_01_001.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 \" \/>\r\nThe 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. When a number is paired with a point, it is called the coordinate of the point.\r\n\r\nThe 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 whole numbers.\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Whole Numbers<\/h3>\r\nThe whole numbers are the counting numbers and zero.\r\n[latex]0,1,2,3,4,5\\ldots[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWe stopped at [latex]5[\/latex] when listing the first few counting numbers and whole numbers. We could have written more numbers if they were needed to make the patterns clear.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWhich of the following are\r\n\r\n[latex]1[\/latex]. counting numbers?\r\n\r\n[latex]2[\/latex]. whole numbers?\r\n<p style=\"padding-left: 60px;\">[latex]0,\\frac{1}{4},3,5.2,15,105[\/latex]<\/p>\r\n&nbsp;\r\n\r\nSolution\r\n<ol>\r\n \t<li>The counting numbers start at [latex]1[\/latex], so [latex]0[\/latex] is not a counting number. The numbers [latex]3,15,\\text{and }105[\/latex] are all counting numbers.<\/li>\r\n \t<li>Whole numbers are counting numbers and [latex]0[\/latex]. The numbers [latex]0,3,15,\\text{and }105[\/latex] are whole numbers.<\/li>\r\n<\/ol>\r\nThe numbers [latex]\\frac{1}{4}[\/latex] and [latex]5.2[\/latex] are neither counting numbers nor whole numbers. We will discuss these numbers later.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]143012[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Model Whole Numbers<\/h2>\r\nOur number system is called a place value system 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] and the [latex]7[\/latex] and the [latex]5[\/latex].\r\n\r\nMoney 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 image below. How much money is in the wallet?\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215158\/CNX_BMath_Figure_01_01_002.png\" alt=\"An image of three stacks of American currency. First stack from left to right is a stack of 3 $100 bills, with label \" \/>\r\nFind the total value of each kind of bill, and then add to find the total. The wallet contains $374.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215200\/CNX_BMath_Figure_01_01_003_img.png\" alt=\"An image of \" \/>\r\nBase-10 blocks provide another way to model place value, as shown in the image below. The blocks can be used to represent hundreds, tens, and ones. Notice 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.\r\n\r\n<img class=\"aligncenter\" 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 \" \/>\r\nThe image below shows the number [latex]138[\/latex] modeled with base-10\u00a0blocks.\r\n\r\nWe use place value notation to show the value of the number [latex]138[\/latex].\r\n\r\n<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 \" \/>\r\n\r\n<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 \" \/>\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><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/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<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nUse place value notation to find the value of the number modeled by the base-10\u00a0blocks shown.\r\n\r\n<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.\" \/>\r\n[reveal-answer q=\"664749\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"664749\"]\r\nThere are [latex]2[\/latex] hundreds squares, which is [latex]200[\/latex].\r\nThere is [latex]1[\/latex] tens rod, which is [latex]10[\/latex].\r\nThere are [latex]5[\/latex] ones blocks, which is [latex]5[\/latex].\r\n<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 \" \/>\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><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]215\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe [latex]\\text{base - 10}[\/latex] blocks model the number [latex]215[\/latex].\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question]143031[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nhttps:\/\/youtu.be\/KcXIxM6h9hk\r\n\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nUse place value notation to find the value of the number modeled by the base-10\u00a0blocks shown.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215211\/CNX_BMath_Figure_01_01_010_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 three horizontal rods containing 10 blocks each. The third item is 7 individual blocks.\" \/>\r\n[reveal-answer q=\"667611\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"667611\"]237[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Identify the Place Value of a Digit<\/h2>\r\nBy looking at money and base-10\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 periods. The periods are <em>ones, thousands, millions, billions, trillions<\/em>, and so on. In a written number, commas separate the periods.\r\n\r\nJust as with the [latex]\\text{base - 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.\r\nThe chart below\u00a0shows how the number [latex]5,278,194[\/latex] is written in a place value chart.\r\n\r\n<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'.\" \/>\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<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nIn the number [latex]63,407,218[\/latex]; find the place value of each of the following digits:\r\n<ol id=\"fs-id2218367\" class=\"circled\">\r\n \t<li>[latex]7[\/latex]<\/li>\r\n \t<li>[latex]0[\/latex]<\/li>\r\n \t<li>[latex]1[\/latex]<\/li>\r\n \t<li>[latex]6[\/latex]<\/li>\r\n \t<li>[latex]3[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"17862\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"17862\"]\r\n\r\nWrite the number in a place value chart, starting at the right.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215216\/CNX_BMath_Figure_01_01_012_img.png\" alt=\"A figure titled \" \/>\r\n<ul id=\"eip-id1168898159450\">\r\n \t<li>The [latex]7[\/latex] is in the thousands place.<\/li>\r\n \t<li>The [latex]0[\/latex] is in the ten thousands place.<\/li>\r\n \t<li>The [latex]1[\/latex] is in the tens place.<\/li>\r\n \t<li>The [latex]6[\/latex] is in the ten millions place.<\/li>\r\n \t<li>The [latex]3[\/latex] is in the millions place.<\/li>\r\n<\/ul>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]130[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nThe video below shows more examples of how to determine the place value of a digit in a number.\r\n\r\nhttps:\/\/youtu.be\/0-4rLGvVEOI","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify the whole numbers from a list of numbers<\/li>\n<li>Identify the counting numbers from a list of numbers<\/li>\n<li>Use place value notation to find the place value of a number modeled by base-10 blocks<\/li>\n<li>Identify the place value of a digit in a number<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Identify Counting Numbers and Whole Numbers<\/h2>\n<p>Learning algebra is similar to learning a language. You start with a basic vocabulary and then add to it as you go along. You need to practice often until the vocabulary becomes easy to you. The more you use the vocabulary, the more familiar it becomes.<\/p>\n<p>Algebra uses numbers and symbols to represent words and ideas. Let\u2019s look at the numbers first. The most basic numbers used in algebra are those we use to count objects: [latex]1,2,3,4,5,\\dots[\/latex] and so on. These are called the counting numbers. The notation &#8220;\u2026&#8221; is called an ellipsis, which is another way to show &#8220;and so on&#8221;, or that the pattern continues endlessly. Counting numbers are also called natural numbers.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Counting Numbers or Natural Numbers<\/h3>\n<p>The counting numbers start with [latex]1[\/latex] and continue.<br \/>\n[latex]1,2,3,4,5\\dots[\/latex]<\/p>\n<\/div>\n<p>Counting numbers and whole numbers can be visualized on a number line as shown below.<\/p>\n<p>The numbers on the number line increase from left to right, and decrease from right to left.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215156\/CNX_BMath_Figure_01_01_001.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\" \/><br \/>\nThe 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. When a number is paired with a point, it is called the coordinate of the point.<\/p>\n<p>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 whole numbers.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Whole Numbers<\/h3>\n<p>The whole numbers are the counting numbers and zero.<br \/>\n[latex]0,1,2,3,4,5\\ldots[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>We stopped at [latex]5[\/latex] when listing the first few counting numbers and whole numbers. We could have written more numbers if they were needed to make the patterns clear.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Which of the following are<\/p>\n<p>[latex]1[\/latex]. counting numbers?<\/p>\n<p>[latex]2[\/latex]. whole numbers?<\/p>\n<p style=\"padding-left: 60px;\">[latex]0,\\frac{1}{4},3,5.2,15,105[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Solution<\/p>\n<ol>\n<li>The counting numbers start at [latex]1[\/latex], so [latex]0[\/latex] is not a counting number. The numbers [latex]3,15,\\text{and }105[\/latex] are all counting numbers.<\/li>\n<li>Whole numbers are counting numbers and [latex]0[\/latex]. The numbers [latex]0,3,15,\\text{and }105[\/latex] are whole numbers.<\/li>\n<\/ol>\n<p>The numbers [latex]\\frac{1}{4}[\/latex] and [latex]5.2[\/latex] are neither counting numbers nor whole numbers. We will discuss these numbers later.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143012\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143012&theme=oea&iframe_resize_id=ohm143012&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Model Whole Numbers<\/h2>\n<p>Our number system is called a place value system 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] and the [latex]7[\/latex] and the [latex]5[\/latex].<\/p>\n<p>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 image below. How much money is in the wallet?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215158\/CNX_BMath_Figure_01_01_002.png\" alt=\"An image of three stacks of American currency. First stack from left to right is a stack of 3 $100 bills, with label\" \/><br \/>\nFind the total value of each kind of bill, and then add to find the total. The wallet contains $374.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215200\/CNX_BMath_Figure_01_01_003_img.png\" alt=\"An image of\" \/><br \/>\nBase-10 blocks provide another way to model place value, as shown in the image below. The blocks can be used to represent hundreds, tens, and ones. Notice 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<p><img decoding=\"async\" class=\"aligncenter\" 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\" \/><br \/>\nThe image below shows the number [latex]138[\/latex] modeled with base-10\u00a0blocks.<\/p>\n<p>We use place value notation to show the value of the number [latex]138[\/latex].<\/p>\n<p><img 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\" \/><\/p>\n<p><img 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\" \/><\/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><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td>[latex]\\text{Sum =}138\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Use place value notation to find the value of the number modeled by the base-10\u00a0blocks shown.<\/p>\n<p><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.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q664749\">Show Solution<\/span><\/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].<br \/>\n<img 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\" \/><\/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><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td>[latex]215\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The [latex]\\text{base - 10}[\/latex] blocks model the number [latex]215[\/latex].\n<\/p><\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143031\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143031&theme=oea&iframe_resize_id=ohm143031&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Determine a Whole Number Given Base 10 Blocks (Hundreds)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/KcXIxM6h9hk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Use place value notation to find the value of the number modeled by the base-10\u00a0blocks shown.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215211\/CNX_BMath_Figure_01_01_010_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 three horizontal rods containing 10 blocks each. The third item is 7 individual blocks.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q667611\">Show Solution<\/span><\/p>\n<div id=\"q667611\" class=\"hidden-answer\" style=\"display: none\">237<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Identify the Place Value of a Digit<\/h2>\n<p>By looking at money and base-10\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 periods. 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 [latex]\\text{base - 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.<br \/>\nThe chart below\u00a0shows how the number [latex]5,278,194[\/latex] is written in a place value chart.<\/p>\n<p><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'.\" \/><\/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<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>In the number [latex]63,407,218[\/latex]; find the place value of each of the following digits:<\/p>\n<ol id=\"fs-id2218367\" class=\"circled\">\n<li>[latex]7[\/latex]<\/li>\n<li>[latex]0[\/latex]<\/li>\n<li>[latex]1[\/latex]<\/li>\n<li>[latex]6[\/latex]<\/li>\n<li>[latex]3[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q17862\">Show Solution<\/span><\/p>\n<div id=\"q17862\" class=\"hidden-answer\" style=\"display: none\">\n<p>Write the number in a place value chart, starting at the right.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215216\/CNX_BMath_Figure_01_01_012_img.png\" alt=\"A figure titled\" \/><\/p>\n<ul id=\"eip-id1168898159450\">\n<li>The [latex]7[\/latex] is in the thousands place.<\/li>\n<li>The [latex]0[\/latex] is in the ten thousands place.<\/li>\n<li>The [latex]1[\/latex] is in the tens place.<\/li>\n<li>The [latex]6[\/latex] is in the ten millions place.<\/li>\n<li>The [latex]3[\/latex] is in the millions place.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm130\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=130&theme=oea&iframe_resize_id=ohm130&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The video below shows more examples of how to determine the place value of a digit in a number.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Examples:  Determining Place Value\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/0-4rLGvVEOI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4591\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Examples: Determining Place Value. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/0-4rLGvVEOI\">https:\/\/youtu.be\/0-4rLGvVEOI<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Determine a Whole Number Given Base 10 Blocks (Hundreds) . <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/KcXIxM6h9hk\">https:\/\/youtu.be\/KcXIxM6h9hk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 143012. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Question ID: 143031. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen 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