{"id":2387,"date":"2021-10-13T15:20:15","date_gmt":"2021-10-13T15:20:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2387"},"modified":"2022-04-24T02:33:55","modified_gmt":"2022-04-24T02:33:55","slug":"comparing-fractions-and-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/comparing-fractions-and-decimals\/","title":{"raw":"Comparing Fractions and Decimals","rendered":"Comparing Fractions and Decimals"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Locate decimals on the number line<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Order decimals and fractions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Locate Decimals On The Number Line<\/h3>\r\nSince decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nLocate [latex]0.4[\/latex] on a number line.\r\n\r\n<strong>Solution<\/strong>\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<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n1. [ohm_question]146228[\/ohm_question]\r\n\r\n2. Locate [latex]0.6[\/latex] on a number line.\r\n\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<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<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<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\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\r\n<h2>Order Decimals and Fractions<\/h2>\r\nIn an earlier lesson, we compared two decimals and determined which was larger. To compare a decimal to a fraction, we will first convert the fraction to a decimal and then compare the decimals.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nOrder [latex]({\\Large\\frac{3}{8}})[\/latex] and [latex](0.4)[\/latex] using [latex]&amp;lt[\/latex] or [latex]\\text{&gt;.}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468630660\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]({\\Large\\frac{3}{8}})[\/latex] [latex](0.4)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]\\Large\\frac{3}{8}[\/latex] to a decimal.<\/td>\r\n<td>[latex](0.375)[\/latex] [latex](0.4)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare [latex]0.375[\/latex] to [latex]0.4[\/latex]<\/td>\r\n<td>[latex]0.375&lt;0.4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite with the original fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{3}{8}}&lt;0.4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146286[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146294[\/ohm_question]\r\n\r\n<\/div>\r\nWatch this video to see more examples of ordering fractions and decimals.\r\n\r\nhttps:\/\/youtu.be\/f4theaYuVuo\r\n\r\n&nbsp;","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Locate decimals on the number line<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Order decimals and fractions<\/li>\n<\/ul>\n<\/div>\n<h3>Locate Decimals On The Number Line<\/h3>\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><strong>Solution<\/strong><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<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>1. <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><\/p>\n<p>2. Locate [latex]0.6[\/latex] on a number line.<\/p>\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<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<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<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>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-1\" 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<h2>Order Decimals and Fractions<\/h2>\n<p>In an earlier lesson, we compared two decimals and determined which was larger. To compare a decimal to a fraction, we will first convert the fraction to a decimal and then compare the decimals.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Order [latex]({\\Large\\frac{3}{8}})[\/latex] and [latex](0.4)[\/latex] using [latex]&lt[\/latex] or [latex]\\text{>.}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468630660\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]({\\Large\\frac{3}{8}})[\/latex] [latex](0.4)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]\\Large\\frac{3}{8}[\/latex] to a decimal.<\/td>\n<td>[latex](0.375)[\/latex] [latex](0.4)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Compare [latex]0.375[\/latex] to [latex]0.4[\/latex]<\/td>\n<td>[latex]0.375<0.4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the original fraction.<\/td>\n<td>[latex]{\\Large\\frac{3}{8}}<0.4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146286\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146286&theme=oea&iframe_resize_id=ohm146286&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146294\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146294&theme=oea&iframe_resize_id=ohm146294&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video to see more examples of ordering fractions and decimals.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Order Fractions and Decimals From Least to Greatest\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/f4theaYuVuo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/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-2387\">\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, 146228, 146286, 146294. <strong>Authored by<\/strong>: de, Vries, S. <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>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li><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>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\">https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/a>. <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>: Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/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><li>Ex: Order Fractions and Decimals From Least to Greatest. <strong>Authored by<\/strong>: Ex: Order Fractions and Decimals From Least to Greatest. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/f4theaYuVuo\">https:\/\/youtu.be\/f4theaYuVuo<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\"},{\"type\":\"cc\",\"description\":\"Decimal Notation: Ordering Decimals\",\"author\":\"James Sousa 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