{"id":63,"date":"2018-03-19T16:26:45","date_gmt":"2018-03-19T16:26:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=63"},"modified":"2024-04-26T22:00:14","modified_gmt":"2024-04-26T22:00:14","slug":"rounding-whole-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/rounding-whole-numbers\/","title":{"raw":"Rounding Whole Numbers","rendered":"Rounding Whole Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Round whole numbers to a determined place value<\/li>\r\n<\/ul>\r\n<\/div>\r\n\r\n[caption id=\"attachment_820\" align=\"alignright\" width=\"406\"]<img class=\"wp-image-820\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/03\/30210033\/1435471427_4f70420e7d_o-300x225.jpg\" alt=\"Image of a Best Buy storefront with people walking along the sidewalk that runs in front of the entrance doors.\" width=\"406\" height=\"308\" \/> Best Buy Storefront[\/caption]\r\n\r\nThe electronics retailer, Best Buy, had [latex]1,026[\/latex] brick and mortar stores open in October of [latex]2016[\/latex].\u00a0Depending on how this information will be used, it might be enough to say that the company has approximately one thousand stores. The word <em style=\"font-size: 16px;\" data-effect=\"italics\">approximately<\/em><span style=\"font-size: 16px;\"> means that one thousand is not the exact count, but is close to the exact value.<\/span>\r\n\r\nIn [latex]2017[\/latex], the social network app, Facebook, reported its annual revenue as [latex]40.7[\/latex] billion US dollars. This could mean they actually brought in [latex]$40,742,985,316[\/latex] or [latex]$40,654,872,131[\/latex]. Sometimes the detail is needed, but sometimes just an approximate value is good enough. The real estate app, Zillow, recorded a profit of [latex]1.07[\/latex] billion US dollars; this is an approximate value. If you want to compare Facebook's [latex]2017[\/latex] revenue with Zillow's [latex]2017[\/latex] revenue, the precise dollars or even millions of dollars are unnecessary.\r\n\r\nThe process of approximating a number is called <strong>rounding<\/strong>. Numbers are rounded to a specific place value depending on how much accuracy is needed. Identifying the number of stores owned by Best Buy as approximately [latex]1[\/latex] thousand means we rounded to the thousands place. Reporting the annual revenue of Facebook as [latex]40.7[\/latex] billion US dollars means we rounded to the hundred millions place. Often the place value to which we round depends on how we will need to use the number.\r\n<p style=\"padding-left: 60px;\">Using a number line can help us visualize and understand the rounding process. Look at the number line below.<\/p>\r\n<p style=\"padding-left: 60px;\">Suppose we want to round the number [latex]76[\/latex] to the nearest ten. Is [latex]76[\/latex] closer to [latex]70[\/latex] ([latex]7[\/latex] tens) or [latex]80[\/latex] ([latex]8[\/latex] tens) on the number line?<\/p>\r\n<p style=\"padding-left: 60px;\">We can see that [latex]76[\/latex] is closer to [latex]80[\/latex] than to [latex]70[\/latex]. So [latex]76[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215230\/CNX_BMath_Figure_01_01_019.png\" alt=\"An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a teal dot at the value 76. \" width=\"975\" height=\"44\" data-media-type=\"image\/png\" \/>\r\n\r\n&nbsp;\r\n<p style=\"padding-left: 60px;\">Now consider the number [latex]72[\/latex]. Find [latex]72[\/latex] on the number line.<\/p>\r\n<p style=\"padding-left: 60px;\">We can see that [latex]72[\/latex] is closer to [latex]70[\/latex], so [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/latex].<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215232\/CNX_BMath_Figure_01_01_020.png\" alt=\"An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a teal dot at the value 72. \" width=\"975\" height=\"44\" data-media-type=\"image\/png\" \/>\r\n\r\n&nbsp;\r\n<p style=\"padding-left: 60px;\">How do we round [latex]75[\/latex] to the nearest ten?<\/p>\r\n<p style=\"padding-left: 60px;\">Find [latex]75[\/latex] on the number line.<\/p>\r\n<p style=\"padding-left: 60px;\">The number [latex]75[\/latex] is exactly midway between [latex]70[\/latex] and [latex]80[\/latex].<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215234\/CNX_BMath_Figure_01_01_021.png\" alt=\"An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a teal dot at the value 75.\" width=\"975\" height=\"44\" data-media-type=\"image\/png\" \/>\r\n<p style=\"padding-left: 60px;\">So that everyone rounds the same way in cases like this, mathematicians have agreed to round up to the higher number. So, [latex]75[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\r\nNow that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than [latex]5[\/latex], round down. If it is greater than or equal to [latex]5[\/latex], round up.\r\n\r\nSo, for example, to round [latex]76[\/latex] to the nearest ten, we look at the digit in the ones place.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215236\/CNX_BMath_Figure_01_01_022.png\" alt=\"An image of value 76, with an arrow pointed at the seven with the label &quot;tens place&quot;, and an arrow pointed at the six with the label &quot;is greater than 5&quot;.\" width=\"210\" height=\"124\" data-media-type=\"image\/png\" \/>\r\nThe digit in the ones place is a [latex]6[\/latex]. Because [latex]6[\/latex] is greater than or equal to [latex]5[\/latex], we increase the digit in the tens place by one. So the [latex]7[\/latex] in the tens place becomes an [latex]8[\/latex]. Now, replace any digits to the right of the [latex]8[\/latex] with zeros. So, [latex]76[\/latex] rounds to [latex]80[\/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\/24215237\/CNX_BMath_Figure_01_01_031_img.png\" alt=\"An image of the value 76 with six slashed through. An arrow points to the six with the label &quot;replace with zero&quot;, and an arrow pointed to the seven with the label &quot;add 1&quot;. Under the 76 is the number 80. The label says &quot;76 rounded to the nearest ten is 80&quot;.\" width=\"286\" height=\"100\" data-media-type=\"image\/png\" \/>\r\nLet\u2019s look again at rounding [latex]72[\/latex] to the nearest [latex]10[\/latex]. Again, we look to the ones place.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215238\/CNX_BMath_Figure_01_01_032_img.png\" alt=\"An image of value 72, with an arrow pointed at the seven with the label &quot;tens place&quot;, and an arrow pointed at the two with the label &quot;is less than 5&quot;.\" width=\"179\" height=\"124\" data-media-type=\"image\/png\" \/>\r\nThe digit in the ones place is [latex]2[\/latex]. Because [latex]2[\/latex] is less than [latex]5[\/latex], we keep the digit in the tens place the same and replace the digits to the right of it with zero. So [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/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\/24215240\/CNX_BMath_Figure_01_01_033_img.png\" alt=\"An image of the value 72 with two slashed through. An arrow points to the two with the label &quot;replace with zero&quot;, and an arrow pointed to the seven with the label &quot;do not add 1&quot;. Under the 72 is the number 70.\" width=\"279\" height=\"66\" data-media-type=\"image\/png\" \/>\r\n\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\" data-type=\"title\">Round a whole number to a specific place value<\/h3>\r\n<ol id=\"eip-id1168287215567\" class=\"stepwise\" data-number-style=\"arabic\">\r\n \t<li>Locate the given place value. All digits to the left of that place value do not change.<\/li>\r\n \t<li>Underline the digit to the right of the given place value.<\/li>\r\n \t<li>Determine if this digit is greater than or equal to [latex]5[\/latex].\r\n<ul id=\"fs-id2486248\" data-bullet-style=\"bullet\">\r\n \t<li>Yes\u2014add [latex]1[\/latex] to the digit in the given place value.<\/li>\r\n \t<li>No\u2014do not change the digit in the given place value.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Replace all digits to the right of the given place value with zeros.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nRound [latex]843[\/latex] to the nearest ten.\r\n\r\nSolution\r\n<table id=\"eip-659\" class=\"unnumbered unstyled\" summary=\"This table is two columns. The first column states locate the tens place. Next to this is the number 843 with the label \">\r\n<tbody>\r\n<tr>\r\n<td data-valign=\"bottom\">Locate the tens place.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215241\/CNX_BMath_Figure_01_01_034_img-01.png\" alt=\"The number 843 with the label &quot;tens place&quot; and an arrow pointing to the 4\" width=\"93\" height=\"78\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Underline the digit to the right of the tens place.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215242\/CNX_BMath_Figure_01_01_034_img-02.png\" alt=\"The number 843 with the 3 underlined.\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since [latex]3[\/latex] is less than [latex]5[\/latex], do not change the digit in the tens place.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215242\/CNX_BMath_Figure_01_01_034_img-03.png\" alt=\"The number 843 with the 3 underlined.\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Replace all digits to the right of the tens place with zeros.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215243\/CNX_BMath_Figure_01_01_034_img-04.png\" alt=\"The number 840 with the 0 underlined.\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rounding [latex]843[\/latex] to the nearest ten gives [latex]840[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]147151[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nRound each number to the nearest hundred:\r\n<ol id=\"eip-id1168287209769\" class=\"circled\" data-number-style=\"lower-alpha\">\r\n \t<li>[latex]23,658[\/latex]<\/li>\r\n \t<li>[latex]3,978[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"210558\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"210558\"]\r\n<table id=\"eip-493\" class=\"unnumbered unstyled\" style=\"width: 745px;\" summary=\"Solution for a. This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states, \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 513.109375px;\">1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 513.109375px;\" data-valign=\"bottom\">Locate the hundreds place.<\/td>\r\n<td style=\"width: 208.890625px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215244\/CNX_BMath_Figure_01_01_035_img-01.png\" alt=\"The number 23,658 with the label &quot;hundreds place&quot; and an arrow pointing to the 6.\" width=\"185\" height=\"69\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 513.109375px;\">The digit of the right of the hundreds place is [latex]5[\/latex]. Underline the digit to the right of the hundreds place.<\/td>\r\n<td style=\"width: 208.890625px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215245\/CNX_BMath_Figure_01_01_035_img-03.png\" alt=\"The number 23,658 with the 5 underlined.\" width=\"213\" height=\"24\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 513.109375px;\">Since [latex]5[\/latex] is greater than or equal to [latex]5[\/latex], round up by adding [latex]1[\/latex] to the digit in the hundreds place. Then replace all digits to the right of the hundreds place with zeros.<\/td>\r\n<td style=\"width: 208.890625px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215246\/CNX_BMath_Figure_01_01_035_img-02.png\" alt=\"Rounding the number 23,658 at the hundreds place. Replace the 5 and 8 with zeros and add one to the 6 to get 23,700.\" width=\"213\" height=\"140\" data-media-type=\"image\/png\" \/>\r\n\r\nSo 23,658 rounded to the nearest hundred is 23,700.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-379\" class=\"unnumbered unstyled\" style=\"width: 745px; height: 303px;\" summary=\"Answer for b. This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states, \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 408px;\">2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 408px;\" data-valign=\"bottom\">Locate the hundreds place.<\/td>\r\n<td style=\"width: 314px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215248\/CNX_BMath_Figure_01_01_036_img-01.png\" alt=\"The number 3,978 with the label &quot;hundreds place&quot; and an arrow pointing to the 9\" width=\"366\" height=\"81\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 408px;\">Underline the digit to the right of the hundreds place.<\/td>\r\n<td style=\"width: 314px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215249\/CNX_BMath_Figure_01_01_036_img-03.png\" alt=\"The number 3,978 with the 7 underlined.\" width=\"371\" height=\"27\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 408px;\">The digit to the right of the hundreds place is [latex]7[\/latex]. Since [latex]7[\/latex] is greater than or equal to [latex]5[\/latex], round up by added [latex]1[\/latex] to the [latex]9[\/latex]. Then place all digits to the right of the hundreds place with zeros.<\/td>\r\n<td style=\"width: 314px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215251\/CNX_BMath_Figure_01_01_036_img-02.png\" alt=\"Rounding the number 3,978 at the hundreds place. Replace the 9 in the hundreds place with 0 and add 1 to the thousands place. Replace the 7 and 8 in the tens and ones place with zeros and you get 4,000.\" width=\"373\" height=\"152\" data-media-type=\"image\/png\" \/>\r\n\r\nSo 3,978 rounded to the nearest hundred is 4,000.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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]147152[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nRound each number to the nearest thousand:\r\n<ol id=\"eip-id1168289456047\" class=\"circled\" data-number-style=\"lower-alpha\">\r\n \t<li>[latex]147,032[\/latex]<\/li>\r\n \t<li>[latex]29,504[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"935310\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"935310\"]\r\n<table id=\"eip-695\" class=\"unnumbered unstyled\" summary=\"This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states, the number 147,032 with the label \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td data-valign=\"bottom\">Locate the thousands place. Underline the digit to the right of the thousands place.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215253\/CNX_BMath_Figure_01_01_037_img-01.png\" alt=\"The number 147,032 with an arrow labeled &quot;Thousand's place&quot; pointing to the 7.\" width=\"155\" height=\"79\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The digit to the right of the thousands place is [latex]0[\/latex]. Since [latex]0[\/latex] is less than [latex]5[\/latex], we do not change the digit in the thousands place.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215254\/CNX_BMath_Figure_01_01_037_img-02.png\" alt=\"The number 147,032 with the 0 underlined.\" width=\"155\" height=\"25\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We then replace all digits to the right of the thousands pace with zeros.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215255\/CNX_BMath_Figure_01_01_037_img-03.png\" alt=\"The number 147,000\" width=\"155\" height=\"25\" data-media-type=\"image\/png\" \/>\r\n\r\nSo 147,032 rounded to the nearest thousand is 147,000.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-596\" class=\"unnumbered unstyled\" style=\"width: 781px; height: 363px;\" summary=\"This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states, locate the thousands place followed by the number 29,504 with the label \" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 15.6562px;\">\r\n<td style=\"height: 15.6562px; width: 439px;\">2.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 35px;\">\r\n<td style=\"height: 35px; width: 439px;\" data-valign=\"bottom\">Locate the thousands place.<\/td>\r\n<td style=\"height: 35px; width: 319px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215256\/CNX_BMath_Figure_01_01_038_img-01.png\" alt=\"The number 29,504 with an arrow labeled &quot;thousands place&quot; pointing to the 9.\" width=\"352\" height=\"80\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 439px;\">Underline the digit to the right of the thousands place.<\/td>\r\n<td style=\"height: 15px; width: 319px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215259\/CNX_BMath_Figure_01_01_038_img-02.png\" alt=\"The number 29,504 with the 5 underlined.\" width=\"358\" height=\"25\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 136px;\">\r\n<td style=\"height: 136px; width: 439px;\">The digit to the right of the thousands place is [latex]5[\/latex]. Since [latex]5[\/latex] is greater than or equal to [latex]5[\/latex], round up by adding [latex]1[\/latex] to the [latex]9[\/latex]. Then replace all digits to the right of the thousands place with zeros.<\/td>\r\n<td style=\"height: 136px; width: 319px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215301\/CNX_BMath_Figure_01_01_038_img-03.png\" alt=\"Rounding the number 29,504 at the thousands place. Replace the 9 in the thousands place with 0 and add 1 to the ten thousands place. Replace the 5, 0, and 4 in the hundreds, tens, and ones places with 0 and the result is 30,000.\" width=\"352\" height=\"150\" data-media-type=\"image\/png\" \/>\r\n\r\nSo 29,504 rounded to the nearest thousand is 30,000.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in part 2, when we add [latex]1[\/latex] thousand to the [latex]9[\/latex] thousands, the total is [latex]10[\/latex] thousands. We regroup this as [latex]1[\/latex] ten thousand and [latex]0[\/latex] thousands. We add the [latex]1[\/latex] ten thousand to the [latex]3[\/latex] ten thousands and put a [latex]0[\/latex] in the thousands place.\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]143029[\/ohm_question]\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]143030[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the video below for more examples of how to round whole numbers to a given place value.\r\n\r\nhttps:\/\/youtu.be\/tpFCYyTi1hc","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Round whole numbers to a determined place value<\/li>\n<\/ul>\n<\/div>\n<div id=\"attachment_820\" style=\"width: 416px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-820\" class=\"wp-image-820\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/03\/30210033\/1435471427_4f70420e7d_o-300x225.jpg\" alt=\"Image of a Best Buy storefront with people walking along the sidewalk that runs in front of the entrance doors.\" width=\"406\" height=\"308\" \/><\/p>\n<p id=\"caption-attachment-820\" class=\"wp-caption-text\">Best Buy Storefront<\/p>\n<\/div>\n<p>The electronics retailer, Best Buy, had [latex]1,026[\/latex] brick and mortar stores open in October of [latex]2016[\/latex].\u00a0Depending on how this information will be used, it might be enough to say that the company has approximately one thousand stores. The word <em style=\"font-size: 16px;\" data-effect=\"italics\">approximately<\/em><span style=\"font-size: 16px;\"> means that one thousand is not the exact count, but is close to the exact value.<\/span><\/p>\n<p>In [latex]2017[\/latex], the social network app, Facebook, reported its annual revenue as [latex]40.7[\/latex] billion US dollars. This could mean they actually brought in [latex]$40,742,985,316[\/latex] or [latex]$40,654,872,131[\/latex]. Sometimes the detail is needed, but sometimes just an approximate value is good enough. The real estate app, Zillow, recorded a profit of [latex]1.07[\/latex] billion US dollars; this is an approximate value. If you want to compare Facebook&#8217;s [latex]2017[\/latex] revenue with Zillow&#8217;s [latex]2017[\/latex] revenue, the precise dollars or even millions of dollars are unnecessary.<\/p>\n<p>The process of approximating a number is called <strong>rounding<\/strong>. Numbers are rounded to a specific place value depending on how much accuracy is needed. Identifying the number of stores owned by Best Buy as approximately [latex]1[\/latex] thousand means we rounded to the thousands place. Reporting the annual revenue of Facebook as [latex]40.7[\/latex] billion US dollars means we rounded to the hundred millions place. Often the place value to which we round depends on how we will need to use the number.<\/p>\n<p style=\"padding-left: 60px;\">Using a number line can help us visualize and understand the rounding process. Look at the number line below.<\/p>\n<p style=\"padding-left: 60px;\">Suppose we want to round the number [latex]76[\/latex] to the nearest ten. Is [latex]76[\/latex] closer to [latex]70[\/latex] ([latex]7[\/latex] tens) or [latex]80[\/latex] ([latex]8[\/latex] tens) on the number line?<\/p>\n<p style=\"padding-left: 60px;\">We can see that [latex]76[\/latex] is closer to [latex]80[\/latex] than to [latex]70[\/latex]. So [latex]76[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215230\/CNX_BMath_Figure_01_01_019.png\" alt=\"An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a teal dot at the value 76.\" width=\"975\" height=\"44\" data-media-type=\"image\/png\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 60px;\">Now consider the number [latex]72[\/latex]. Find [latex]72[\/latex] on the number line.<\/p>\n<p style=\"padding-left: 60px;\">We can see that [latex]72[\/latex] is closer to [latex]70[\/latex], so [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/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\/24215232\/CNX_BMath_Figure_01_01_020.png\" alt=\"An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a teal dot at the value 72.\" width=\"975\" height=\"44\" data-media-type=\"image\/png\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"padding-left: 60px;\">How do we round [latex]75[\/latex] to the nearest ten?<\/p>\n<p style=\"padding-left: 60px;\">Find [latex]75[\/latex] on the number line.<\/p>\n<p style=\"padding-left: 60px;\">The number [latex]75[\/latex] is exactly midway between [latex]70[\/latex] and [latex]80[\/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\/24215234\/CNX_BMath_Figure_01_01_021.png\" alt=\"An image of a number line from 70 to 80 with increments of one. All the numbers on the number line are black except for 70 and 80 which are red. There is a teal dot at the value 75.\" width=\"975\" height=\"44\" data-media-type=\"image\/png\" \/><\/p>\n<p style=\"padding-left: 60px;\">So that everyone rounds the same way in cases like this, mathematicians have agreed to round up to the higher number. So, [latex]75[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\n<p>Now that we have looked at this process on the number line, we can introduce a more general procedure. To round a number to a specific place, look at the number to the right of that place. If the number is less than [latex]5[\/latex], round down. If it is greater than or equal to [latex]5[\/latex], round up.<\/p>\n<p>So, for example, to round [latex]76[\/latex] to the nearest ten, we look at the digit in the ones place.<\/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\/24215236\/CNX_BMath_Figure_01_01_022.png\" alt=\"An image of value 76, with an arrow pointed at the seven with the label &quot;tens place&quot;, and an arrow pointed at the six with the label &quot;is greater than 5&quot;.\" width=\"210\" height=\"124\" data-media-type=\"image\/png\" \/><br \/>\nThe digit in the ones place is a [latex]6[\/latex]. Because [latex]6[\/latex] is greater than or equal to [latex]5[\/latex], we increase the digit in the tens place by one. So the [latex]7[\/latex] in the tens place becomes an [latex]8[\/latex]. Now, replace any digits to the right of the [latex]8[\/latex] with zeros. So, [latex]76[\/latex] rounds to [latex]80[\/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\/24215237\/CNX_BMath_Figure_01_01_031_img.png\" alt=\"An image of the value 76 with six slashed through. An arrow points to the six with the label &quot;replace with zero&quot;, and an arrow pointed to the seven with the label &quot;add 1&quot;. Under the 76 is the number 80. The label says &quot;76 rounded to the nearest ten is 80&quot;.\" width=\"286\" height=\"100\" data-media-type=\"image\/png\" \/><br \/>\nLet\u2019s look again at rounding [latex]72[\/latex] to the nearest [latex]10[\/latex]. Again, we look to the ones place.<\/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\/24215238\/CNX_BMath_Figure_01_01_032_img.png\" alt=\"An image of value 72, with an arrow pointed at the seven with the label &quot;tens place&quot;, and an arrow pointed at the two with the label &quot;is less than 5&quot;.\" width=\"179\" height=\"124\" data-media-type=\"image\/png\" \/><br \/>\nThe digit in the ones place is [latex]2[\/latex]. Because [latex]2[\/latex] is less than [latex]5[\/latex], we keep the digit in the tens place the same and replace the digits to the right of it with zero. So [latex]72[\/latex] rounded to the nearest ten is [latex]70[\/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\/24215240\/CNX_BMath_Figure_01_01_033_img.png\" alt=\"An image of the value 72 with two slashed through. An arrow points to the two with the label &quot;replace with zero&quot;, and an arrow pointed to the seven with the label &quot;do not add 1&quot;. Under the 72 is the number 70.\" width=\"279\" height=\"66\" data-media-type=\"image\/png\" \/><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\" data-type=\"title\">Round a whole number to a specific place value<\/h3>\n<ol id=\"eip-id1168287215567\" class=\"stepwise\" data-number-style=\"arabic\">\n<li>Locate the given place value. All digits to the left of that place value do not change.<\/li>\n<li>Underline the digit to the right of the given place value.<\/li>\n<li>Determine if this digit is greater than or equal to [latex]5[\/latex].\n<ul id=\"fs-id2486248\" data-bullet-style=\"bullet\">\n<li>Yes\u2014add [latex]1[\/latex] to the digit in the given place value.<\/li>\n<li>No\u2014do not change the digit in the given place value.<\/li>\n<\/ul>\n<\/li>\n<li>Replace all digits to the right of the given place value with zeros.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Round [latex]843[\/latex] to the nearest ten.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-659\" class=\"unnumbered unstyled\" summary=\"This table is two columns. The first column states locate the tens place. Next to this is the number 843 with the label\">\n<tbody>\n<tr>\n<td data-valign=\"bottom\">Locate the tens place.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215241\/CNX_BMath_Figure_01_01_034_img-01.png\" alt=\"The number 843 with the label &quot;tens place&quot; and an arrow pointing to the 4\" width=\"93\" height=\"78\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Underline the digit to the right of the tens place.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215242\/CNX_BMath_Figure_01_01_034_img-02.png\" alt=\"The number 843 with the 3 underlined.\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Since [latex]3[\/latex] is less than [latex]5[\/latex], do not change the digit in the tens place.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215242\/CNX_BMath_Figure_01_01_034_img-03.png\" alt=\"The number 843 with the 3 underlined.\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Replace all digits to the right of the tens place with zeros.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215243\/CNX_BMath_Figure_01_01_034_img-04.png\" alt=\"The number 840 with the 0 underlined.\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rounding [latex]843[\/latex] to the nearest ten gives [latex]840[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm147151\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=147151&theme=oea&iframe_resize_id=ohm147151\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Round each number to the nearest hundred:<\/p>\n<ol id=\"eip-id1168287209769\" class=\"circled\" data-number-style=\"lower-alpha\">\n<li>[latex]23,658[\/latex]<\/li>\n<li>[latex]3,978[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q210558\">Show Answer<\/span><\/p>\n<div id=\"q210558\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-493\" class=\"unnumbered unstyled\" style=\"width: 745px;\" summary=\"Solution for a. This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states,\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 513.109375px;\">1.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 513.109375px;\" data-valign=\"bottom\">Locate the hundreds place.<\/td>\n<td style=\"width: 208.890625px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215244\/CNX_BMath_Figure_01_01_035_img-01.png\" alt=\"The number 23,658 with the label &quot;hundreds place&quot; and an arrow pointing to the 6.\" width=\"185\" height=\"69\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 513.109375px;\">The digit of the right of the hundreds place is [latex]5[\/latex]. Underline the digit to the right of the hundreds place.<\/td>\n<td style=\"width: 208.890625px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215245\/CNX_BMath_Figure_01_01_035_img-03.png\" alt=\"The number 23,658 with the 5 underlined.\" width=\"213\" height=\"24\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 513.109375px;\">Since [latex]5[\/latex] is greater than or equal to [latex]5[\/latex], round up by adding [latex]1[\/latex] to the digit in the hundreds place. Then replace all digits to the right of the hundreds place with zeros.<\/td>\n<td style=\"width: 208.890625px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215246\/CNX_BMath_Figure_01_01_035_img-02.png\" alt=\"Rounding the number 23,658 at the hundreds place. Replace the 5 and 8 with zeros and add one to the 6 to get 23,700.\" width=\"213\" height=\"140\" data-media-type=\"image\/png\" \/><\/p>\n<p>So 23,658 rounded to the nearest hundred is 23,700.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-379\" class=\"unnumbered unstyled\" style=\"width: 745px; height: 303px;\" summary=\"Answer for b. This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states,\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 408px;\">2.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 408px;\" data-valign=\"bottom\">Locate the hundreds place.<\/td>\n<td style=\"width: 314px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215248\/CNX_BMath_Figure_01_01_036_img-01.png\" alt=\"The number 3,978 with the label &quot;hundreds place&quot; and an arrow pointing to the 9\" width=\"366\" height=\"81\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 408px;\">Underline the digit to the right of the hundreds place.<\/td>\n<td style=\"width: 314px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215249\/CNX_BMath_Figure_01_01_036_img-03.png\" alt=\"The number 3,978 with the 7 underlined.\" width=\"371\" height=\"27\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 408px;\">The digit to the right of the hundreds place is [latex]7[\/latex]. Since [latex]7[\/latex] is greater than or equal to [latex]5[\/latex], round up by added [latex]1[\/latex] to the [latex]9[\/latex]. Then place all digits to the right of the hundreds place with zeros.<\/td>\n<td style=\"width: 314px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215251\/CNX_BMath_Figure_01_01_036_img-02.png\" alt=\"Rounding the number 3,978 at the hundreds place. Replace the 9 in the hundreds place with 0 and add 1 to the thousands place. Replace the 7 and 8 in the tens and ones place with zeros and you get 4,000.\" width=\"373\" height=\"152\" data-media-type=\"image\/png\" \/><\/p>\n<p>So 3,978 rounded to the nearest hundred is 4,000.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm147152\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=147152&theme=oea&iframe_resize_id=ohm147152\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Round each number to the nearest thousand:<\/p>\n<ol id=\"eip-id1168289456047\" class=\"circled\" data-number-style=\"lower-alpha\">\n<li>[latex]147,032[\/latex]<\/li>\n<li>[latex]29,504[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q935310\">Show Answer<\/span><\/p>\n<div id=\"q935310\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-695\" class=\"unnumbered unstyled\" summary=\"This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states, the number 147,032 with the label\" data-label=\"\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"bottom\">Locate the thousands place. Underline the digit to the right of the thousands place.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215253\/CNX_BMath_Figure_01_01_037_img-01.png\" alt=\"The number 147,032 with an arrow labeled &quot;Thousand's place&quot; pointing to the 7.\" width=\"155\" height=\"79\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>The digit to the right of the thousands place is [latex]0[\/latex]. Since [latex]0[\/latex] is less than [latex]5[\/latex], we do not change the digit in the thousands place.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215254\/CNX_BMath_Figure_01_01_037_img-02.png\" alt=\"The number 147,032 with the 0 underlined.\" width=\"155\" height=\"25\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td>We then replace all digits to the right of the thousands pace with zeros.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215255\/CNX_BMath_Figure_01_01_037_img-03.png\" alt=\"The number 147,000\" width=\"155\" height=\"25\" data-media-type=\"image\/png\" \/><\/p>\n<p>So 147,032 rounded to the nearest thousand is 147,000.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-596\" class=\"unnumbered unstyled\" style=\"width: 781px; height: 363px;\" summary=\"This table is set in two columns. The left column is annotated and the right column shows numbers. In the left column, it states, locate the thousands place followed by the number 29,504 with the label\" data-label=\"\">\n<tbody>\n<tr style=\"height: 15.6562px;\">\n<td style=\"height: 15.6562px; width: 439px;\">2.<\/td>\n<\/tr>\n<tr style=\"height: 35px;\">\n<td style=\"height: 35px; width: 439px;\" data-valign=\"bottom\">Locate the thousands place.<\/td>\n<td style=\"height: 35px; width: 319px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215256\/CNX_BMath_Figure_01_01_038_img-01.png\" alt=\"The number 29,504 with an arrow labeled &quot;thousands place&quot; pointing to the 9.\" width=\"352\" height=\"80\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 439px;\">Underline the digit to the right of the thousands place.<\/td>\n<td style=\"height: 15px; width: 319px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215259\/CNX_BMath_Figure_01_01_038_img-02.png\" alt=\"The number 29,504 with the 5 underlined.\" width=\"358\" height=\"25\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr style=\"height: 136px;\">\n<td style=\"height: 136px; width: 439px;\">The digit to the right of the thousands place is [latex]5[\/latex]. Since [latex]5[\/latex] is greater than or equal to [latex]5[\/latex], round up by adding [latex]1[\/latex] to the [latex]9[\/latex]. Then replace all digits to the right of the thousands place with zeros.<\/td>\n<td style=\"height: 136px; width: 319px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215301\/CNX_BMath_Figure_01_01_038_img-03.png\" alt=\"Rounding the number 29,504 at the thousands place. Replace the 9 in the thousands place with 0 and add 1 to the ten thousands place. Replace the 5, 0, and 4 in the hundreds, tens, and ones places with 0 and the result is 30,000.\" width=\"352\" height=\"150\" data-media-type=\"image\/png\" \/><\/p>\n<p>So 29,504 rounded to the nearest thousand is 30,000.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that in part 2, when we add [latex]1[\/latex] thousand to the [latex]9[\/latex] thousands, the total is [latex]10[\/latex] thousands. We regroup this as [latex]1[\/latex] ten thousand and [latex]0[\/latex] thousands. We add the [latex]1[\/latex] ten thousand to the [latex]3[\/latex] ten thousands and put a [latex]0[\/latex] in the thousands place.\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143029\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143029&theme=oea&iframe_resize_id=ohm143029\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143030\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143030&theme=oea&iframe_resize_id=ohm143030\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the video below for more examples of how to round whole numbers to a given place value.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Rounding to the Various Place Values - Number Line \/ Formal Rules\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/tpFCYyTi1hc?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-63\">\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>Question ID: 143029, 143030. <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>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>Ex: Rounding to the Various Place Values - Number Line \/ Formal Rules . <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/tpFCYyTi1hc\">https:\/\/youtu.be\/tpFCYyTi1hc<\/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><strong>Authored by<\/strong>: Ian Muttoo. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.flickr.com\/photos\/imuttoo\/1435471427\">https:\/\/www.flickr.com\/photos\/imuttoo\/1435471427<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/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":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Question ID: 143029, 143030\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex: Rounding to the Various Place Values - 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