{"id":3912,"date":"2020-02-11T03:26:37","date_gmt":"2020-02-11T03:26:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3912"},"modified":"2021-02-05T23:56:51","modified_gmt":"2021-02-05T23:56:51","slug":"locating-and-ordering-decimals-with-a-number-line","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/locating-and-ordering-decimals-with-a-number-line\/","title":{"raw":"Locating and Ordering Decimals With a Number Line","rendered":"Locating and Ordering Decimals With a Number Line"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Locate decimals on a number line<\/li>\r\n \t<li>Order decimals using inequality notation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nLocate [latex]0.4[\/latex] on a number line.\r\n\r\nSolution\r\nThe decimal [latex]0.4[\/latex] is equivalent to [latex]{\\Large\\frac{4}{10}}[\/latex], so [latex]0.4[\/latex] is located between [latex]0[\/latex] and [latex]1[\/latex]. On a number line, divide the interval between [latex]0[\/latex] and [latex]1[\/latex] into [latex]10[\/latex] equal parts and place marks to separate the parts.\r\n\r\nLabel the marks [latex]0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0[\/latex]. We write [latex]0[\/latex] as [latex]0.0[\/latex] and [latex]1[\/latex] as [latex]1.0[\/latex], so that the numbers are consistently in tenths. Finally, mark [latex]0.4[\/latex] on the number line.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221458\/CNX_BMath_Figure_05_01_010_img.png\" alt=\"A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot at 0.4.\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<ol>\r\n \t<li>[ohm_question]146228[\/ohm_question]<\/li>\r\n \t<li>Locate [latex]0.6[\/latex] on a number line.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"4936\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"4936\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221500\/CNX_BMath_Figure_05_01_005_img.png\" alt=\"This image shows a number line from 0.0 to 1.0 and segmented into tenths. A point is plotted at 0.6 on the number line.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nLocate [latex]-0.74[\/latex] on a number line.\r\n[reveal-answer q=\"669401\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"669401\"]\r\n\r\nSolution\r\nThe decimal [latex]-0.74[\/latex] is equivalent to [latex]-{\\Large\\frac{74}{100}}[\/latex], so it is located between [latex]0[\/latex] and [latex]-1[\/latex]. On a number line, mark off and label the multiples of [latex]-0.10[\/latex] in the interval between [latex]0[\/latex] and [latex]-1[\/latex] ( [latex]-0.10[\/latex] , [latex]-0.20[\/latex] , etc.) and mark [latex]-0.74[\/latex] between [latex]-0.70[\/latex] and [latex]-0.80[\/latex], a little closer to [latex]-0.70[\/latex] .\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221503\/CNX_BMath_Figure_05_01_007_img.png\" alt=\"A number line is shown with negative 1.00, negative 0.90, negative 0.80, negative 0.70, negative 0.60, negative 0.50, negative 0.40, negative 0.30, negative 0.20, negative 0.10, and 0.00 labeled. There is a red dot between negative 0.80 and negative 0.70 labeled as negative 0.74.\" \/>\r\n\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]146577[\/ohm_question]\r\n\r\n[ohm_question]146578[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show more examples of how to locate a decimal on the number line.\r\n\r\nhttps:\/\/youtu.be\/F3LAKsOBdNA\r\n<h3>Order Decimals<\/h3>\r\nWhich is larger, [latex]0.04[\/latex] or [latex]0.40?[\/latex]\r\n\r\nIf you think of this as money, you know that [latex]$0.40[\/latex] (forty cents) is greater than [latex]$0.04[\/latex] (four cents). So,\r\n<p style=\"text-align: center\">[latex]0.40&gt;0.04[\/latex]<\/p>\r\nIn previous chapters, we used the number line to order numbers.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ a&lt;b\\text{ , }a\\text{ is less than }b\\text{ when }a\\text{ is to the left of }b\\text{ on the number line}\\hfill \\\\ a&gt;b\\text{ , }a\\text{ is greater than }b\\text{ when }a\\text{ is to the right of }b\\text{ on the number line}\\hfill \\end{array}[\/latex]<\/p>\r\nWhere are [latex]0.04[\/latex] and [latex]0.40[\/latex] located on the number line?\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221458\/CNX_BMath_Figure_05_01_010_img.png\" alt=\"A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot between 0.0 and 0.1 labeled as 0.04. There is another red dot at 0.4.\" \/>\r\nWe see that [latex]0.40[\/latex] is to the right of [latex]0.04[\/latex]. So we know [latex]0.40&gt;0.04[\/latex].\r\n\r\nHow does [latex]0.31[\/latex] compare to [latex]0.308?[\/latex] This doesn\u2019t translate into money to make the comparison easy. But if we convert [latex]0.31[\/latex] and [latex]0.308[\/latex] to fractions, we can tell which is larger.\r\n<table id=\"eip-id1168466250128\" class=\"unnumbered unstyled\" summary=\"The numbers 0.31 and 0.308 are shown. The first step says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0.31[\/latex]<\/td>\r\n<td>[latex]0.308[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to fractions.<\/td>\r\n<td>[latex]{\\Large\\frac{31}{100}}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{308}{1000}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We need a common denominator to compare them.<\/td>\r\n<td>[latex]{\\Large\\frac{31\\cdot\\color{red}{10}}{100\\cdot\\color{red}{10}}}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{308}{1000}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{310}{1000}}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{308}{1000}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nBecause [latex]310&gt;308[\/latex], we know that [latex]{\\Large\\frac{310}{1000}}&gt;{\\Large\\frac{308}{1000}}[\/latex]. Therefore, [latex]0.31&gt;0.308[\/latex].\r\n\r\nNotice what we did in converting [latex]0.31[\/latex] to a fraction\u2014we started with the fraction [latex]\\Large\\frac{31}{100}[\/latex] and ended with the equivalent fraction [latex]\\Large\\frac{310}{1000}[\/latex]. Converting [latex]\\Large\\frac{310}{1000}[\/latex] back to a decimal gives [latex]0.310[\/latex]. So [latex]0.31[\/latex] is equivalent to [latex]0.310[\/latex]. Writing zeros at the end of a decimal does not change its value.\r\n<p style=\"text-align: center\">[latex]{\\Large\\frac{31}{100}}={\\Large\\frac{310}{1000}}\\text{ and }0.31=0.310[\/latex]<\/p>\r\nIf two decimals have the same value, they are said to be equivalent decimals.\r\n<p style=\"text-align: center\">[latex]0.31=0.310[\/latex]<\/p>\r\nWe say [latex]0.31[\/latex] and [latex]0.310[\/latex] are equivalent decimals.\r\n<div class=\"textbox shaded\">\r\n<h3>Equivalent Decimals<\/h3>\r\nTwo decimals are equivalent decimals if they convert to equivalent fractions.\r\n\r\n<\/div>\r\nRemember, writing zeros at the end of a decimal does not change its value.\r\n<div class=\"textbox shaded\">\r\n<h3>Order decimals<\/h3>\r\n<ol id=\"eip-id1168468520524\" class=\"stepwise\">\r\n \t<li>Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.<\/li>\r\n \t<li>Compare the numbers to the right of the decimal point as if they were whole numbers.<\/li>\r\n \t<li>Order the numbers using the appropriate inequality sign.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nOrder the following decimals using [latex]&lt;\\text{ or }\\text{&gt;}[\/latex]:\r\n<ol>\r\n \t<li>[latex]0.64[\/latex] ____ [latex]0.6[\/latex]<\/li>\r\n \t<li>[latex]0.83[\/latex] ____ [latex]0.803[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"895615\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"895615\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466266395\" class=\"unnumbered unstyled\" style=\"width: 859px\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 494.5px\">1.<\/td>\r\n<td style=\"width: 341.5px\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 494.5px\"><\/td>\r\n<td style=\"width: 341.5px\">[latex]0.64[\/latex] ____ [latex]0.6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 494.5px\">Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of [latex]0.6[\/latex].<\/td>\r\n<td style=\"width: 341.5px\">[latex]0.64[\/latex] ____ [latex]0.6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 494.5px\">Compare the numbers to the right of the decimal point as if they were whole numbers.<\/td>\r\n<td style=\"width: 341.5px\">[latex]64&gt;60[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 494.5px\">Order the numbers using the appropriate inequality sign.<\/td>\r\n<td style=\"width: 341.5px\">[latex]0.64&gt;0.60[\/latex]\r\n\r\n[latex]0.64&gt;0.6[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468466609\" class=\"unnumbered unstyled\" style=\"width: 859px\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 500.45px\">2.<\/td>\r\n<td style=\"width: 334.55px\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 500.45px\"><\/td>\r\n<td style=\"width: 334.55px\">[latex]0.83[\/latex] ____ [latex]0.803[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 500.45px\">Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of [latex]0.83[\/latex].<\/td>\r\n<td style=\"width: 334.55px\">[latex]0.83[\/latex] ____ [latex]0.803[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 500.45px\">Compare the numbers to the right of the decimal point as if they were whole numbers.<\/td>\r\n<td style=\"width: 334.55px\">[latex]830&gt;803[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 500.45px\">Order the numbers using the appropriate inequality sign.<\/td>\r\n<td style=\"width: 334.55px\">[latex]0.830&gt;0.803[\/latex]\r\n\r\n[latex]0.83&gt;0.803[\/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]146232[\/ohm_question]\r\n\r\n[ohm_question]146237[\/ohm_question]\r\n\r\n[ohm_question]146238[\/ohm_question]\r\n\r\n<\/div>\r\nWhen we order negative decimals, it is important to remember how to order negative integers. Recall that larger numbers are to the right on the number line. For example, because [latex]-2[\/latex] lies to the right of [latex]-3[\/latex] on the number line, we know that [latex]-2&gt;-3[\/latex]. Similarly, smaller numbers lie to the left on the number line. For example, because [latex]-9[\/latex] lies to the left of [latex]-6[\/latex] on the number line, we know that [latex]-9&lt;-6[\/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\/24221509\/CNX_BMath_Figure_05_01_018_img.png\" alt=\"A number line is shown with integers from negative 10 to 0. Blue dots are placed on negative nine and negative six. Red dots are placed at negative two and negative three.\" \/>\r\nIf we zoomed in on the interval between [latex]0[\/latex] and [latex]-1[\/latex], we would see in the same way that [latex]-0.2&gt;-0.3\\text{and}-0.9&lt;-0.6[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nUse [latex]&lt;\\text{or}&amp;gt[\/latex]; to order. [latex]-0.1[\/latex] ____ [latex]- 0.8[\/latex].\r\n[reveal-answer q=\"12939\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"12939\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468485697\" class=\"unnumbered unstyled\" style=\"width: 770px\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 461.067px\"><\/td>\r\n<td style=\"width: 283.933px\">[latex]-0.1[\/latex] ____ [latex]- 0.8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 461.067px\">Write the numbers one under the other, lining up the decimal points.<\/td>\r\n<td style=\"width: 283.933px\">[latex]-0.1[\/latex]\r\n\r\n[latex]-0.8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 461.067px\">They have the same number of digits.<\/td>\r\n<td style=\"width: 283.933px\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 461.067px\">Since [latex]-1&gt;-8,-1[\/latex] tenth is greater than [latex]-8[\/latex] tenths.<\/td>\r\n<td style=\"width: 283.933px\">[latex]-0.1&gt;-0.8[\/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]146239[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video lesson we show how to order decimals using inequality notation by comparing place values, and by using fractions.\r\n\r\nhttps:\/\/youtu.be\/fjO3fnt3ABA","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Locate decimals on a number line<\/li>\n<li>Order decimals using inequality notation<\/li>\n<\/ul>\n<\/div>\n<p>Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Locate [latex]0.4[\/latex] on a number line.<\/p>\n<p>Solution<br \/>\nThe decimal [latex]0.4[\/latex] is equivalent to [latex]{\\Large\\frac{4}{10}}[\/latex], so [latex]0.4[\/latex] is located between [latex]0[\/latex] and [latex]1[\/latex]. On a number line, divide the interval between [latex]0[\/latex] and [latex]1[\/latex] into [latex]10[\/latex] equal parts and place marks to separate the parts.<\/p>\n<p>Label the marks [latex]0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0[\/latex]. We write [latex]0[\/latex] as [latex]0.0[\/latex] and [latex]1[\/latex] as [latex]1.0[\/latex], so that the numbers are consistently in tenths. Finally, mark [latex]0.4[\/latex] on the number line.<\/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\/24221458\/CNX_BMath_Figure_05_01_010_img.png\" alt=\"A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot at 0.4.\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<ol>\n<li><iframe loading=\"lazy\" id=\"ohm146228\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146228&theme=oea&iframe_resize_id=ohm146228&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/li>\n<li>Locate [latex]0.6[\/latex] on a number line.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q4936\">Show Solution<\/span><\/p>\n<div id=\"q4936\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221500\/CNX_BMath_Figure_05_01_005_img.png\" alt=\"This image shows a number line from 0.0 to 1.0 and segmented into tenths. A point is plotted at 0.6 on the number line.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Locate [latex]-0.74[\/latex] on a number line.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q669401\">Show Solution<\/span><\/p>\n<div id=\"q669401\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nThe decimal [latex]-0.74[\/latex] is equivalent to [latex]-{\\Large\\frac{74}{100}}[\/latex], so it is located between [latex]0[\/latex] and [latex]-1[\/latex]. On a number line, mark off and label the multiples of [latex]-0.10[\/latex] in the interval between [latex]0[\/latex] and [latex]-1[\/latex] ( [latex]-0.10[\/latex] , [latex]-0.20[\/latex] , etc.) and mark [latex]-0.74[\/latex] between [latex]-0.70[\/latex] and [latex]-0.80[\/latex], a little closer to [latex]-0.70[\/latex] .<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221503\/CNX_BMath_Figure_05_01_007_img.png\" alt=\"A number line is shown with negative 1.00, negative 0.90, negative 0.80, negative 0.70, negative 0.60, negative 0.50, negative 0.40, negative 0.30, negative 0.20, negative 0.10, and 0.00 labeled. There is a red dot between negative 0.80 and negative 0.70 labeled as negative 0.74.\" \/><\/p>\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=\"ohm146577\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146577&theme=oea&iframe_resize_id=ohm146577&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146578\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146578&theme=oea&iframe_resize_id=ohm146578&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show more examples of how to locate a decimal on the number line.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Example:  Identify Decimals on the Number Line\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/F3LAKsOBdNA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Order Decimals<\/h3>\n<p>Which is larger, [latex]0.04[\/latex] or [latex]0.40?[\/latex]<\/p>\n<p>If you think of this as money, you know that [latex]$0.40[\/latex] (forty cents) is greater than [latex]$0.04[\/latex] (four cents). So,<\/p>\n<p style=\"text-align: center\">[latex]0.40>0.04[\/latex]<\/p>\n<p>In previous chapters, we used the number line to order numbers.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{}\\\\ a<b\\text{ , }a\\text{ is less than }b\\text{ when }a\\text{ is to the left of }b\\text{ on the number line}\\hfill \\\\ a>b\\text{ , }a\\text{ is greater than }b\\text{ when }a\\text{ is to the right of }b\\text{ on the number line}\\hfill \\end{array}[\/latex]<\/p>\n<p>Where are [latex]0.04[\/latex] and [latex]0.40[\/latex] located on the number line?<\/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\/24221458\/CNX_BMath_Figure_05_01_010_img.png\" alt=\"A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot between 0.0 and 0.1 labeled as 0.04. There is another red dot at 0.4.\" \/><br \/>\nWe see that [latex]0.40[\/latex] is to the right of [latex]0.04[\/latex]. So we know [latex]0.40>0.04[\/latex].<\/p>\n<p>How does [latex]0.31[\/latex] compare to [latex]0.308?[\/latex] This doesn\u2019t translate into money to make the comparison easy. But if we convert [latex]0.31[\/latex] and [latex]0.308[\/latex] to fractions, we can tell which is larger.<\/p>\n<table id=\"eip-id1168466250128\" class=\"unnumbered unstyled\" summary=\"The numbers 0.31 and 0.308 are shown. The first step says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]0.31[\/latex]<\/td>\n<td>[latex]0.308[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to fractions.<\/td>\n<td>[latex]{\\Large\\frac{31}{100}}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{308}{1000}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We need a common denominator to compare them.<\/td>\n<td>[latex]{\\Large\\frac{31\\cdot\\color{red}{10}}{100\\cdot\\color{red}{10}}}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{308}{1000}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{310}{1000}}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{308}{1000}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Because [latex]310>308[\/latex], we know that [latex]{\\Large\\frac{310}{1000}}>{\\Large\\frac{308}{1000}}[\/latex]. Therefore, [latex]0.31>0.308[\/latex].<\/p>\n<p>Notice what we did in converting [latex]0.31[\/latex] to a fraction\u2014we started with the fraction [latex]\\Large\\frac{31}{100}[\/latex] and ended with the equivalent fraction [latex]\\Large\\frac{310}{1000}[\/latex]. Converting [latex]\\Large\\frac{310}{1000}[\/latex] back to a decimal gives [latex]0.310[\/latex]. So [latex]0.31[\/latex] is equivalent to [latex]0.310[\/latex]. Writing zeros at the end of a decimal does not change its value.<\/p>\n<p style=\"text-align: center\">[latex]{\\Large\\frac{31}{100}}={\\Large\\frac{310}{1000}}\\text{ and }0.31=0.310[\/latex]<\/p>\n<p>If two decimals have the same value, they are said to be equivalent decimals.<\/p>\n<p style=\"text-align: center\">[latex]0.31=0.310[\/latex]<\/p>\n<p>We say [latex]0.31[\/latex] and [latex]0.310[\/latex] are equivalent decimals.<\/p>\n<div class=\"textbox shaded\">\n<h3>Equivalent Decimals<\/h3>\n<p>Two decimals are equivalent decimals if they convert to equivalent fractions.<\/p>\n<\/div>\n<p>Remember, writing zeros at the end of a decimal does not change its value.<\/p>\n<div class=\"textbox shaded\">\n<h3>Order decimals<\/h3>\n<ol id=\"eip-id1168468520524\" class=\"stepwise\">\n<li>Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.<\/li>\n<li>Compare the numbers to the right of the decimal point as if they were whole numbers.<\/li>\n<li>Order the numbers using the appropriate inequality sign.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Order the following decimals using [latex]<\\text{ or }\\text{>}[\/latex]:<\/p>\n<ol>\n<li>[latex]0.64[\/latex] ____ [latex]0.6[\/latex]<\/li>\n<li>[latex]0.83[\/latex] ____ [latex]0.803[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q895615\">Show Solution<\/span><\/p>\n<div id=\"q895615\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466266395\" class=\"unnumbered unstyled\" style=\"width: 859px\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 494.5px\">1.<\/td>\n<td style=\"width: 341.5px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 494.5px\"><\/td>\n<td style=\"width: 341.5px\">[latex]0.64[\/latex] ____ [latex]0.6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 494.5px\">Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of [latex]0.6[\/latex].<\/td>\n<td style=\"width: 341.5px\">[latex]0.64[\/latex] ____ [latex]0.6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 494.5px\">Compare the numbers to the right of the decimal point as if they were whole numbers.<\/td>\n<td style=\"width: 341.5px\">[latex]64>60[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 494.5px\">Order the numbers using the appropriate inequality sign.<\/td>\n<td style=\"width: 341.5px\">[latex]0.64>0.60[\/latex]<\/p>\n<p>[latex]0.64>0.6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468466609\" class=\"unnumbered unstyled\" style=\"width: 859px\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 500.45px\">2.<\/td>\n<td style=\"width: 334.55px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 500.45px\"><\/td>\n<td style=\"width: 334.55px\">[latex]0.83[\/latex] ____ [latex]0.803[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 500.45px\">Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of [latex]0.83[\/latex].<\/td>\n<td style=\"width: 334.55px\">[latex]0.83[\/latex] ____ [latex]0.803[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 500.45px\">Compare the numbers to the right of the decimal point as if they were whole numbers.<\/td>\n<td style=\"width: 334.55px\">[latex]830>803[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 500.45px\">Order the numbers using the appropriate inequality sign.<\/td>\n<td style=\"width: 334.55px\">[latex]0.830>0.803[\/latex]<\/p>\n<p>[latex]0.83>0.803[\/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=\"ohm146232\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146232&theme=oea&iframe_resize_id=ohm146232&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146237\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146237&theme=oea&iframe_resize_id=ohm146237&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146238\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146238&theme=oea&iframe_resize_id=ohm146238&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>When we order negative decimals, it is important to remember how to order negative integers. Recall that larger numbers are to the right on the number line. For example, because [latex]-2[\/latex] lies to the right of [latex]-3[\/latex] on the number line, we know that [latex]-2>-3[\/latex]. Similarly, smaller numbers lie to the left on the number line. For example, because [latex]-9[\/latex] lies to the left of [latex]-6[\/latex] on the number line, we know that [latex]-9<-6[\/latex].\n\n<img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221509\/CNX_BMath_Figure_05_01_018_img.png\" alt=\"A number line is shown with integers from negative 10 to 0. Blue dots are placed on negative nine and negative six. Red dots are placed at negative two and negative three.\" \/><br \/>\nIf we zoomed in on the interval between [latex]0[\/latex] and [latex]-1[\/latex], we would see in the same way that [latex]-0.2>-0.3\\text{and}-0.9<-0.6[\/latex].\n\n\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Use [latex]<\\text{or}&gt[\/latex]; to order. [latex]-0.1[\/latex] ____ [latex]- 0.8[\/latex].\n\n\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q12939\">Show Solution<\/span><\/p>\n<div id=\"q12939\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468485697\" class=\"unnumbered unstyled\" style=\"width: 770px\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 461.067px\"><\/td>\n<td style=\"width: 283.933px\">[latex]-0.1[\/latex] ____ [latex]- 0.8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 461.067px\">Write the numbers one under the other, lining up the decimal points.<\/td>\n<td style=\"width: 283.933px\">[latex]-0.1[\/latex]<\/p>\n<p>[latex]-0.8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 461.067px\">They have the same number of digits.<\/td>\n<td style=\"width: 283.933px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 461.067px\">Since [latex]-1>-8,-1[\/latex] tenth is greater than [latex]-8[\/latex] tenths.<\/td>\n<td style=\"width: 283.933px\">[latex]-0.1>-0.8[\/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=\"ohm146239\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146239&theme=oea&iframe_resize_id=ohm146239&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video lesson we show how to order decimals using inequality notation by comparing place values, and by using fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Decimal Notation:  Ordering Decimals\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/fjO3fnt3ABA?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-3912\">\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 146237, 146238, 146239. <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><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Example: Identify Decimals on the Number Line. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/F3LAKsOBdNA\">https:\/\/youtu.be\/F3LAKsOBdNA<\/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>Decimal Notation: Ordering Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/fjO3fnt3ABA\">https:\/\/youtu.be\/fjO3fnt3ABA<\/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":25777,"menu_order":5,"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\":\"Example: Identify Decimals on the Number Line\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/F3LAKsOBdNA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Decimal Notation: Ordering Decimals\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/fjO3fnt3ABA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146237, 146238, 146239\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3912","chapter","type-chapter","status-web-only","hentry"],"part":377,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3912","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\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3912\/revisions"}],"predecessor-version":[{"id":3913,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3912\/revisions\/3913"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/377"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3912\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3912"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3912"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3912"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}