{"id":4593,"date":"2020-04-21T00:19:04","date_gmt":"2020-04-21T00:19:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/rounding-whole-numbers\/"},"modified":"2024-06-26T17:36:13","modified_gmt":"2024-06-26T17:36:13","slug":"rounding-whole-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/rounding-whole-numbers\/","title":{"raw":"Rounding Whole Numbers","rendered":"Rounding Whole Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify the place value of a digit used for rounding<\/li>\r\n \t<li>Round a whole number to a specific place value<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\nIn [latex]2013[\/latex], the U.S. Census Bureau reported the population of the state of New York as [latex]19,651,127[\/latex] people. It might be enough to say that the population is approximately [latex]20[\/latex] million. The word <em style=\"font-size: 16px;\">approximately<\/em><span style=\"font-size: 16px;\"> means that [latex]20[\/latex] million is not the exact population, but is close to the exact value.<\/span>\r\n\r\nThe process of approximating a number is called rounding. Numbers are rounded to a specific place value depending on how much accuracy is needed. Saying that the population of New York is approximately [latex]20[\/latex] million means we rounded to the millions place. The place value to which we round to depends on how we need to use the number.\r\n\r\nUsing the number line can help you visualize and understand the rounding process. Look at the number line below. Suppose we want to round the number [latex]76[\/latex] to the nearest ten. Is [latex]76[\/latex] closer to [latex]70[\/latex] or [latex]80[\/latex] on the number line?\r\n\r\nWe 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].\r\n\r\n<img 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 an orange dot at the value \" \/>\r\n\r\n&nbsp;\r\n\r\nNow consider the number [latex]72[\/latex]. Find [latex]72[\/latex] on the number line.\r\n\r\nWe 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].\r\n\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 an orange dot at the value \" \/>\r\n\r\n&nbsp;\r\n\r\nHow do we round [latex]75[\/latex] to the nearest ten?\r\n\r\nFind [latex]75[\/latex] on the number line.\r\n\r\nThe number [latex]75[\/latex] is exactly midway between [latex]70[\/latex] and [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\/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 an orange dot at the value \" \/>\r\nSo that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, [latex]80[\/latex]. So, [latex]75[\/latex] rounded to the nearest ten is [latex]80[\/latex].\r\n\r\n&nbsp;\r\n\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 \" \/>\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 \" \/>\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 \" \/>\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 \" \/>\r\n\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Round a whole number to a specific place value<\/h3>\r\n<ol id=\"eip-id1168287215567\" class=\"stepwise\">\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\">\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 examples\">\r\n<h3>TIp For Success<\/h3>\r\nIf the digit to the right of your given place value is 5 or above, give your given place value a shove.\r\n\r\nIf the digit to the right of your given place value is 4 or less, let your given place value rest.\r\n\r\n<\/div>\r\n&nbsp;\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>Locate 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\/24215241\/CNX_BMath_Figure_01_01_034_img-01.png\" alt=\"The number 843 with the label \" \/><\/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.\" \/><\/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.\" \/><\/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.\" \/><\/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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]147151[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\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\">\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 Solution[\/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, \">\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;\">Locate the hundreds place.<\/td>\r\n<td style=\"width: 208.890625px;\"><img class=\"\" 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=\"..\" width=\"185\" height=\"69\" \/><\/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 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=\"..\" \/><\/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 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=\"..\" \/>\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: 911px;\" 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, \">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 501.75px;\">2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 501.75px;\">Locate the hundreds place.<\/td>\r\n<td style=\"width: 390.25px;\"><img class=\"\" 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=\"..\" width=\"366\" height=\"81\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 501.75px;\">Underline the digit to the right of the hundreds place.<\/td>\r\n<td style=\"width: 390.25px;\"><img class=\"\" 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=\"..\" width=\"371\" height=\"27\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 501.75px;\">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: 390.25px;\"><img class=\"\" 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=\"..\" width=\"373\" height=\"152\" \/>\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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]147152[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\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\">\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 Solution[\/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 \">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Locate the thousands place. Underline the digit to the right of the thousands place.<\/td>\r\n<td><img 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=\"..\" \/><\/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 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=\"..\" \/><\/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 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=\"..\" \/>\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: 745px;\" 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 \">\r\n<tbody>\r\n<tr style=\"height: 15.6562px;\">\r\n<td style=\"height: 15.6562px; width: 418.078125px;\">2.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 35px;\">\r\n<td style=\"height: 35px; width: 418.078125px;\">Locate the thousands place.<\/td>\r\n<td style=\"height: 35px; width: 303.921875px;\"><img 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=\"..\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"height: 15px; width: 418.078125px;\">Underline the digit to the right of the thousands place.<\/td>\r\n<td style=\"height: 15px; width: 303.921875px;\"><img 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=\"..\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 136px;\">\r\n<td style=\"height: 136px; width: 418.078125px;\">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: 303.921875px;\"><img 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=\"..\" \/>\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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143029[\/ohm_question]\r\n\r\n[ohm_question]143030[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWhat 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 Outcomes<\/h3>\n<ul>\n<li>Identify the place value of a digit used for rounding<\/li>\n<li>Round a whole number to a specific place value<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In [latex]2013[\/latex], the U.S. Census Bureau reported the population of the state of New York as [latex]19,651,127[\/latex] people. It might be enough to say that the population is approximately [latex]20[\/latex] million. The word <em style=\"font-size: 16px;\">approximately<\/em><span style=\"font-size: 16px;\"> means that [latex]20[\/latex] million is not the exact population, but is close to the exact value.<\/span><\/p>\n<p>The process of approximating a number is called rounding. Numbers are rounded to a specific place value depending on how much accuracy is needed. Saying that the population of New York is approximately [latex]20[\/latex] million means we rounded to the millions place. The place value to which we round to depends on how we need to use the number.<\/p>\n<p>Using the number line can help you visualize and understand the rounding process. Look at the number line below. Suppose we want to round the number [latex]76[\/latex] to the nearest ten. Is [latex]76[\/latex] closer to [latex]70[\/latex] or [latex]80[\/latex] on the number line?<\/p>\n<p>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 decoding=\"async\" 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 an orange dot at the value\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Now consider the number [latex]72[\/latex]. Find [latex]72[\/latex] on the number line.<\/p>\n<p>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 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 an orange dot at the value\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>How do we round [latex]75[\/latex] to the nearest ten?<\/p>\n<p>Find [latex]75[\/latex] on the number line.<\/p>\n<p>The number [latex]75[\/latex] is exactly midway between [latex]70[\/latex] and [latex]80[\/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\/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 an orange dot at the value\" \/><br \/>\nSo that everyone rounds the same way in cases like this, mathematicians have agreed to round to the higher number, [latex]80[\/latex]. So, [latex]75[\/latex] rounded to the nearest ten is [latex]80[\/latex].<\/p>\n<p>&nbsp;<\/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 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\" \/><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 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\" \/><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 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\" \/><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 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\" \/><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Round a whole number to a specific place value<\/h3>\n<ol id=\"eip-id1168287215567\" class=\"stepwise\">\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\">\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 examples\">\n<h3>TIp For Success<\/h3>\n<p>If the digit to the right of your given place value is 5 or above, give your given place value a shove.<\/p>\n<p>If the digit to the right of your given place value is 4 or less, let your given place value rest.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\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>Locate 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\/24215241\/CNX_BMath_Figure_01_01_034_img-01.png\" alt=\"The number 843 with the label\" \/><\/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.\" \/><\/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.\" \/><\/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.\" \/><\/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<p>&nbsp;<\/p>\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&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\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\">\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 Solution<\/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,\">\n<tbody>\n<tr>\n<td style=\"width: 513.109375px;\">1.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 513.109375px;\">Locate the hundreds place.<\/td>\n<td style=\"width: 208.890625px;\"><img loading=\"lazy\" decoding=\"async\" class=\"\" 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=\"..\" width=\"185\" height=\"69\" \/><\/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 decoding=\"async\" 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=\"..\" \/><\/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 decoding=\"async\" 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=\"..\" \/><\/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: 911px;\" 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,\">\n<tbody>\n<tr>\n<td style=\"width: 501.75px;\">2.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 501.75px;\">Locate the hundreds place.<\/td>\n<td style=\"width: 390.25px;\"><img loading=\"lazy\" decoding=\"async\" class=\"\" 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=\"..\" width=\"366\" height=\"81\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 501.75px;\">Underline the digit to the right of the hundreds place.<\/td>\n<td style=\"width: 390.25px;\"><img loading=\"lazy\" decoding=\"async\" class=\"\" 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=\"..\" width=\"371\" height=\"27\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 501.75px;\">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: 390.25px;\"><img loading=\"lazy\" decoding=\"async\" class=\"\" 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=\"..\" width=\"373\" height=\"152\" \/><\/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<p>&nbsp;<\/p>\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&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\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\">\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 Solution<\/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\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>Locate the thousands place. Underline the digit to the right of the thousands place.<\/td>\n<td><img decoding=\"async\" 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=\"..\" \/><\/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 decoding=\"async\" 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=\"..\" \/><\/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 decoding=\"async\" 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=\"..\" \/><\/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: 745px;\" 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\">\n<tbody>\n<tr style=\"height: 15.6562px;\">\n<td style=\"height: 15.6562px; width: 418.078125px;\">2.<\/td>\n<\/tr>\n<tr style=\"height: 35px;\">\n<td style=\"height: 35px; width: 418.078125px;\">Locate the thousands place.<\/td>\n<td style=\"height: 35px; width: 303.921875px;\"><img decoding=\"async\" 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=\"..\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"height: 15px; width: 418.078125px;\">Underline the digit to the right of the thousands place.<\/td>\n<td style=\"height: 15px; width: 303.921875px;\"><img decoding=\"async\" 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=\"..\" \/><\/td>\n<\/tr>\n<tr style=\"height: 136px;\">\n<td style=\"height: 136px; width: 418.078125px;\">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: 303.921875px;\"><img decoding=\"async\" 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=\"..\" \/><\/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<p>&nbsp;<\/p>\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&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm143030\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143030&theme=oea&iframe_resize_id=ohm143030&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>What 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-4593\">\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>Authored by<\/strong>: Deborah Devlin. <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>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>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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Authored 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><\/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":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"Deborah Devlin\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Rounding to the Various Place Values - Number Line \/ Formal Rules \",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/tpFCYyTi1hc\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"OpenStax\",\"organization\":\"\",\"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\":\"Question ID: 143029, 143030\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4593","chapter","type-chapter","status-publish","hentry"],"part":5569,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4593","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4593\/revisions"}],"predecessor-version":[{"id":5576,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4593\/revisions\/5576"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/5569"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4593\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4593"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4593"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4593"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}