{"id":294,"date":"2023-06-05T15:30:39","date_gmt":"2023-06-05T15:30:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/rounding-decimals\/"},"modified":"2023-07-11T17:35:00","modified_gmt":"2023-07-11T17:35:00","slug":"rounding-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/rounding-decimals\/","title":{"raw":"Rounding Decimals - Optional Section (This is for review)","rendered":"Rounding Decimals &#8211; Optional Section (This is for review)"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Round a decimal to a given place value<\/li>\r\n<\/ul>\r\n<\/div>\r\nThere will be several times when working problems in the Percents and Finance Unit where you will be asked to round your answers.\u00a0 This section is to help you review how to round decimals.\r\n\r\nIn the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at [latex]\\$3.279[\/latex] per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay [latex]$3.28[\/latex] , because the final price would be rounded to the nearest cent.\r\n\r\nSuppose we wanted to round [latex]$2.72[\/latex] to the nearest dollar. Is it closer to [latex]$2[\/latex] or to [latex]$3[\/latex]? What if we wanted to round [latex]$2.72[\/latex] to the nearest ten cents; is it closer to [latex]$2.70[\/latex] or to [latex]$2.80[\/latex]? The number lines in the image below can help us answer those questions.\r\n\r\n(a) We see that [latex]2.72[\/latex] is closer to [latex]3[\/latex] than to [latex]2[\/latex]. So, [latex]2.72[\/latex] rounded to the nearest whole number is [latex]3[\/latex].\r\n\r\n(b) We see that [latex]2.72[\/latex] is closer to [latex]2.70[\/latex] than [latex]2.80[\/latex]. So we say that [latex]2.72[\/latex] rounded to the nearest tenth is [latex]2.7[\/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\/24221512\/CNX_BMath_Figure_05_01_012.png\" alt=\"In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72. In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72. \" \/>\r\nCan we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.\r\n<div class=\"textbox shaded\">\r\n<h3>Round a decimal.<\/h3>\r\n<ol class=\"stepwise\">\r\n \t<li>Locate the given place value and mark it with an arrow.<\/li>\r\n \t<li>Underline the digit to the right of the given place value.<\/li>\r\n \t<li>Is this digit greater than or equal to [latex]5?[\/latex]\r\n<ul>\r\n \t<li>Yes - add [latex]1[\/latex] to the digit in the given place value.<\/li>\r\n \t<li>No - do not change the digit in the given place value<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Rewrite the number, removing all digits to the right of the given place value.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n\r\n<span style=\"color: #3366ff;\">Tip:\u00a0 If the digit to the right of your given place value is 5 or above, give your given place value a shove.\u00a0 If the digit to the right of your given place value is 4 or less, let your given place value rest.<\/span>\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nRound [latex]18.379[\/latex] to the nearest hundredth.\r\n\r\nSolution\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]18.379[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Locate the hundredths place and mark it with an arrow.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221515\/CNX_BMath_Figure_05_01_021_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Underline the digit to the right of the [latex]7[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221516\/CNX_BMath_Figure_05_01_021_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Because [latex]9[\/latex] is greater than or equal to [latex]5[\/latex], add [latex]1[\/latex] to the [latex]7[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221517\/CNX_BMath_Figure_05_01_021_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the number, deleting all digits to the right of the hundredths place.<\/td>\r\n<td>[latex]18.38[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]18.38[\/latex] is [latex]18.379[\/latex] rounded to the nearest hundredth.<\/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]146242[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nRound [latex]18.379[\/latex] to the nearest\r\n<ol>\r\n \t<li>tenth<\/li>\r\n \t<li>whole number\r\n[reveal-answer q=\"414963\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"414963\"]<\/li>\r\n<\/ol>\r\nSolution\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>1. Round [latex]18.379[\/latex] to the nearest tenth.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]18.379[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Locate the tenths place and mark it with an arrow.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221520\/CNX_BMath_Figure_05_01_022_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Underline the digit to the right of the tenths digit.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221521\/CNX_BMath_Figure_05_01_022_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Because [latex]7[\/latex] is greater than or equal to [latex]5[\/latex], add [latex]1[\/latex] to the [latex]3[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221523\/CNX_BMath_Figure_05_01_022_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the number, deleting all digits to the right of the tenths place.<\/td>\r\n<td>[latex]18.4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, [latex]18.379[\/latex] rounded to the nearest tenth is [latex]18.4[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>2. Round [latex]18.379[\/latex] to the nearest whole number.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]18.379[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Locate the ones place and mark it with an arrow.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221526\/CNX_BMath_Figure_05_01_023_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Underline the digit to the right of the ones place.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221527\/CNX_BMath_Figure_05_01_023_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since [latex]3[\/latex] is not greater than or equal to [latex]5[\/latex], do not add [latex]1[\/latex] to the [latex]8[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221528\/CNX_BMath_Figure_05_01_023_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the number, deleting all digits to the right of the ones place.<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So [latex]18.379[\/latex] rounded to the nearest whole number is [latex]18[\/latex].<\/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]146244[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see an example of how to round a number to several different place values.\r\n\r\nhttps:\/\/youtu.be\/qu4Y9DGqXlk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Round a decimal to a given place value<\/li>\n<\/ul>\n<\/div>\n<p>There will be several times when working problems in the Percents and Finance Unit where you will be asked to round your answers.\u00a0 This section is to help you review how to round decimals.<\/p>\n<p>In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at [latex]\\$3.279[\/latex] per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay [latex]$3.28[\/latex] , because the final price would be rounded to the nearest cent.<\/p>\n<p>Suppose we wanted to round [latex]$2.72[\/latex] to the nearest dollar. Is it closer to [latex]$2[\/latex] or to [latex]$3[\/latex]? What if we wanted to round [latex]$2.72[\/latex] to the nearest ten cents; is it closer to [latex]$2.70[\/latex] or to [latex]$2.80[\/latex]? The number lines in the image below can help us answer those questions.<\/p>\n<p>(a) We see that [latex]2.72[\/latex] is closer to [latex]3[\/latex] than to [latex]2[\/latex]. So, [latex]2.72[\/latex] rounded to the nearest whole number is [latex]3[\/latex].<\/p>\n<p>(b) We see that [latex]2.72[\/latex] is closer to [latex]2.70[\/latex] than [latex]2.80[\/latex]. So we say that [latex]2.72[\/latex] rounded to the nearest tenth is [latex]2.7[\/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\/24221512\/CNX_BMath_Figure_05_01_012.png\" alt=\"In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72. In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72.\" \/><br \/>\nCan we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.<\/p>\n<div class=\"textbox shaded\">\n<h3>Round a decimal.<\/h3>\n<ol class=\"stepwise\">\n<li>Locate the given place value and mark it with an arrow.<\/li>\n<li>Underline the digit to the right of the given place value.<\/li>\n<li>Is this digit greater than or equal to [latex]5?[\/latex]\n<ul>\n<li>Yes &#8211; add [latex]1[\/latex] to the digit in the given place value.<\/li>\n<li>No &#8211; do not change the digit in the given place value<\/li>\n<\/ul>\n<\/li>\n<li>Rewrite the number, removing all digits to the right of the given place value.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #3366ff;\">Tip:\u00a0 If the digit to the right of your given place value is 5 or above, give your given place value a shove.\u00a0 If the digit to the right of your given place value is 4 or less, let your given place value rest.<\/span><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Round [latex]18.379[\/latex] to the nearest hundredth.<\/p>\n<p>Solution<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]18.379[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Locate the hundredths place and mark it with an arrow.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221515\/CNX_BMath_Figure_05_01_021_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Underline the digit to the right of the [latex]7[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221516\/CNX_BMath_Figure_05_01_021_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Because [latex]9[\/latex] is greater than or equal to [latex]5[\/latex], add [latex]1[\/latex] to the [latex]7[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221517\/CNX_BMath_Figure_05_01_021_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the number, deleting all digits to the right of the hundredths place.<\/td>\n<td>[latex]18.38[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]18.38[\/latex] is [latex]18.379[\/latex] rounded to the nearest hundredth.<\/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=\"ohm146242\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146242&theme=oea&iframe_resize_id=ohm146242&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 [latex]18.379[\/latex] to the nearest<\/p>\n<ol>\n<li>tenth<\/li>\n<li>whole number\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q414963\">Show Solution<\/span><\/p>\n<div id=\"q414963\" class=\"hidden-answer\" style=\"display: none\"><\/li>\n<\/ol>\n<p>Solution<\/p>\n<table>\n<tbody>\n<tr>\n<td>1. Round [latex]18.379[\/latex] to the nearest tenth.<\/td>\n<\/tr>\n<tr>\n<td>[latex]18.379[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Locate the tenths place and mark it with an arrow.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221520\/CNX_BMath_Figure_05_01_022_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Underline the digit to the right of the tenths digit.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221521\/CNX_BMath_Figure_05_01_022_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Because [latex]7[\/latex] is greater than or equal to [latex]5[\/latex], add [latex]1[\/latex] to the [latex]3[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221523\/CNX_BMath_Figure_05_01_022_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the number, deleting all digits to the right of the tenths place.<\/td>\n<td>[latex]18.4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>So, [latex]18.379[\/latex] rounded to the nearest tenth is [latex]18.4[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td>2. Round [latex]18.379[\/latex] to the nearest whole number.<\/td>\n<\/tr>\n<tr>\n<td>[latex]18.379[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Locate the ones place and mark it with an arrow.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221526\/CNX_BMath_Figure_05_01_023_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Underline the digit to the right of the ones place.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221527\/CNX_BMath_Figure_05_01_023_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Since [latex]3[\/latex] is not greater than or equal to [latex]5[\/latex], do not add [latex]1[\/latex] to the [latex]8[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221528\/CNX_BMath_Figure_05_01_023_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the number, deleting all digits to the right of the ones place.<\/td>\n<td>[latex]18[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>So [latex]18.379[\/latex] rounded to the nearest whole number is [latex]18[\/latex].<\/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=\"ohm146244\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146244&theme=oea&iframe_resize_id=ohm146244&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see an example of how to round a number to several different place values.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Examples:  Rounding Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/qu4Y9DGqXlk?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-294\">\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>Question ID 146239, 146242, 146244. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Examples: Rounding Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/qu4Y9DGqXlk\">https:\/\/youtu.be\/qu4Y9DGqXlk<\/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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><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><\/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":503070,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"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\":\"Examples: Rounding Decimals\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/qu4Y9DGqXlk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146239, 146242, 146244\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + 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