{"id":61,"date":"2018-03-19T16:25:49","date_gmt":"2018-03-19T16:25:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=61"},"modified":"2024-04-26T22:00:04","modified_gmt":"2024-04-26T22:00:04","slug":"place-value","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/place-value\/","title":{"raw":"Place Value in Whole Numbers","rendered":"Place Value in Whole Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Use place value to define all digits of a whole number<\/li>\r\n<\/ul>\r\n<\/div>\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, then a stack of 7 $10 bills, then a stack of 4 $1 bills. 3 time $100 equals $300, 7 times $10 equals $70, and 4 times $1 equals $4.\" width=\"597\" height=\"219\" data-media-type=\"image\/png\" \/>\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=\"$300 plus $70 plus $4 equals $374\" width=\"126\" height=\"90\" data-media-type=\"image\/png\" \/>\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 &quot;A single block represents 1&quot;. The second item is row of ten squares with the label &quot;A rod represents 10&quot;. The third items is a square made up of smaller squares with the label &quot;A square represents 100&quot;.\" width=\"347\" height=\"287\" data-media-type=\"image\/png\" \/>\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 1 hundred. Then 3 separate rows of squares with the label 3 tens. Then 8 single squares with the label 8 ones.\" width=\"431\" height=\"152\" data-media-type=\"image\/png\" \/>\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=\"The equation 100 plus 30 plus 8. Taking the hundredth's, tenth's and one's place from each number, respectively, the sum is 138.\" width=\"97\" height=\"93\" data-media-type=\"image\/png\" \/>\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.\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"center\">Digit<\/th>\r\n<th data-align=\"center\">Place value<\/th>\r\n<th data-align=\"center\">Number<\/th>\r\n<th data-align=\"center\">Value<\/th>\r\n<th data-align=\"right\">Total value<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\r\n<td data-align=\"center\">hundreds<\/td>\r\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]100[\/latex]<\/td>\r\n<td data-align=\"right\">[latex]100\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]3[\/latex]<\/td>\r\n<td data-align=\"center\">tens<\/td>\r\n<td data-align=\"center\">[latex]3[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]10[\/latex]<\/td>\r\n<td data-align=\"right\">[latex]30\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]8[\/latex]<\/td>\r\n<td data-align=\"center\">ones<\/td>\r\n<td data-align=\"center\">[latex]8[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\r\n<td data-align=\"right\">[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 data-align=\"right\">[latex]\\text{Sum =}138\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h3><\/h3>\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.\" data-media-type=\"image\/png\" \/>\r\n[reveal-answer q=\"664749\"]Show Answer[\/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=\"The equation 200 plus 10 plus 5. Taking the hundredth's, tenth's and one's place from each number, respectively, the sum is 215.\" width=\"97\" height=\"89\" data-media-type=\"image\/png\" \/>\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.\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"center\">Digit<\/th>\r\n<th data-align=\"center\">Place value<\/th>\r\n<th data-align=\"center\">Number<\/th>\r\n<th data-align=\"center\">Value<\/th>\r\n<th data-align=\"right\">Total value<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]2[\/latex]<\/td>\r\n<td data-align=\"center\">hundreds<\/td>\r\n<td data-align=\"center\">[latex]2[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]100[\/latex]<\/td>\r\n<td data-align=\"right\">[latex]200\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\r\n<td data-align=\"center\">tens<\/td>\r\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]10[\/latex]<\/td>\r\n<td data-align=\"right\">[latex]10\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\">[latex]5[\/latex]<\/td>\r\n<td data-align=\"center\">ones<\/td>\r\n<td data-align=\"center\">[latex]5[\/latex]<\/td>\r\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\r\n<td data-align=\"right\">[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 data-align=\"right\">[latex]215\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe base-[latex]10[\/latex] blocks model the number [latex]215[\/latex].\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question hide_question_numbers=1]143031[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/KcXIxM6h9hk\r\n\r\nBy looking at money and base-[latex]10[\/latex] blocks, 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 data-effect=\"italics\">ones, thousands, millions, billions, trillions<\/em>, and so on. In a written number, commas separate the periods.\r\n\r\nJust 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.\r\n\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'.\" data-media-type=\"image\/png\" \/>\r\n<ul id=\"fs-id930962\" data-bullet-style=\"bullet\">\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\" data-number-style=\"lower-alpha\">\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 Answer[\/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 with each digit separated out from the number 63,407,218, and each place value is labeled.\" width=\"431\" height=\"297\" data-media-type=\"image\/png\" \/>\r\n<ul id=\"eip-id1168898159450\" data-labeled-item=\"true\">\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<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]130[\/ohm_question]\r\n\r\n<\/div>\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 Objectives<\/h3>\n<ul>\n<li>Use place value to define all digits of a whole number<\/li>\n<\/ul>\n<\/div>\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 loading=\"lazy\" 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, then a stack of 7 $10 bills, then a stack of 4 $1 bills. 3 time $100 equals $300, 7 times $10 equals $70, and 4 times $1 equals $4.\" width=\"597\" height=\"219\" data-media-type=\"image\/png\" \/><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 loading=\"lazy\" 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=\"$300 plus $70 plus $4 equals $374\" width=\"126\" height=\"90\" data-media-type=\"image\/png\" \/><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 loading=\"lazy\" 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 &quot;A single block represents 1&quot;. The second item is row of ten squares with the label &quot;A rod represents 10&quot;. The third items is a square made up of smaller squares with the label &quot;A square represents 100&quot;.\" width=\"347\" height=\"287\" data-media-type=\"image\/png\" \/><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 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 1 hundred. Then 3 separate rows of squares with the label 3 tens. Then 8 single squares with the label 8 ones.\" width=\"431\" height=\"152\" data-media-type=\"image\/png\" \/><\/p>\n<p><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=\"The equation 100 plus 30 plus 8. Taking the hundredth's, tenth's and one's place from each number, respectively, the sum is 138.\" width=\"97\" height=\"93\" data-media-type=\"image\/png\" \/><\/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.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Digit<\/th>\n<th data-align=\"center\">Place value<\/th>\n<th data-align=\"center\">Number<\/th>\n<th data-align=\"center\">Value<\/th>\n<th data-align=\"right\">Total value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\n<td data-align=\"center\">hundreds<\/td>\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\n<td data-align=\"center\">[latex]100[\/latex]<\/td>\n<td data-align=\"right\">[latex]100\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]3[\/latex]<\/td>\n<td data-align=\"center\">tens<\/td>\n<td data-align=\"center\">[latex]3[\/latex]<\/td>\n<td data-align=\"center\">[latex]10[\/latex]<\/td>\n<td data-align=\"right\">[latex]30\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]8[\/latex]<\/td>\n<td data-align=\"center\">ones<\/td>\n<td data-align=\"center\">[latex]8[\/latex]<\/td>\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\n<td data-align=\"right\">[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 data-align=\"right\">[latex]\\text{Sum =}138\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><\/h3>\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.\" data-media-type=\"image\/png\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q664749\">Show Answer<\/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 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=\"The equation 200 plus 10 plus 5. Taking the hundredth's, tenth's and one's place from each number, respectively, the sum is 215.\" width=\"97\" height=\"89\" data-media-type=\"image\/png\" \/><\/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.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Digit<\/th>\n<th data-align=\"center\">Place value<\/th>\n<th data-align=\"center\">Number<\/th>\n<th data-align=\"center\">Value<\/th>\n<th data-align=\"right\">Total value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]2[\/latex]<\/td>\n<td data-align=\"center\">hundreds<\/td>\n<td data-align=\"center\">[latex]2[\/latex]<\/td>\n<td data-align=\"center\">[latex]100[\/latex]<\/td>\n<td data-align=\"right\">[latex]200\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\n<td data-align=\"center\">tens<\/td>\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\n<td data-align=\"center\">[latex]10[\/latex]<\/td>\n<td data-align=\"right\">[latex]10\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\">[latex]5[\/latex]<\/td>\n<td data-align=\"center\">ones<\/td>\n<td data-align=\"center\">[latex]5[\/latex]<\/td>\n<td data-align=\"center\">[latex]1[\/latex]<\/td>\n<td data-align=\"right\">[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 data-align=\"right\">[latex]215\\phantom{\\rule{1 em}{0ex}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The base-[latex]10[\/latex] blocks model the number [latex]215[\/latex].\n<\/p><\/div>\n<\/div>\n<\/div>\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\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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>By looking at money and base-[latex]10[\/latex] blocks, 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 data-effect=\"italics\">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<p>The 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'.\" data-media-type=\"image\/png\" \/><\/p>\n<ul id=\"fs-id930962\" data-bullet-style=\"bullet\">\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\" data-number-style=\"lower-alpha\">\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 Answer<\/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 loading=\"lazy\" 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 with each digit separated out from the number 63,407,218, and each place value is labeled.\" width=\"431\" height=\"297\" data-media-type=\"image\/png\" \/><\/p>\n<ul id=\"eip-id1168898159450\" data-labeled-item=\"true\">\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<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\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-61\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><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>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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><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><\/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":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Examples: Determining Place Value\",\"author\":\"James Sousa 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