{"id":3929,"date":"2020-02-11T04:23:37","date_gmt":"2020-02-11T04:23:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3929"},"modified":"2021-02-05T23:57:04","modified_gmt":"2021-02-05T23:57:04","slug":"comparing-decimals-and-fractions","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/comparing-decimals-and-fractions\/","title":{"raw":"Comparing Decimals and Fractions","rendered":"Comparing Decimals and Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Order fractions and decimals by writing fractions as decimals<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Order Decimals and Fractions<\/h2>\r\nIn and 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}}) (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}}) (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) (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&nbsp;\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\nWhen ordering negative numbers, remember that larger numbers are to the right on the number line and any positive number is greater than any negative number.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nOrder [latex](-0.5) (-{\\Large\\frac{3}{4}})[\/latex] using [latex]&amp;lt[\/latex]; or [latex]\\text{&gt;.}[\/latex]\r\n[reveal-answer q=\"677046\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"677046\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466186266\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex](-0.5) (-{\\Large\\frac{3}{4}})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]-{\\Large\\frac{3}{4}}[\/latex] to a decimal.<\/td>\r\n<td>[latex](-0.5) (- 0.75)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Compare [latex]-0.5[\/latex] to [latex]-0.75[\/latex] .<\/td>\r\n<td>[latex]-0.5&gt;-0.75[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the inequality with the original fraction.<\/td>\r\n<td>[latex]-0.5&gt;-{\\Large\\frac{3}{4}}[\/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]146290[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite the numbers [latex]{\\Large\\frac{13}{20}},0.61,{\\Large\\frac{11}{16}}[\/latex] in order from smallest to largest.\r\n[reveal-answer q=\"509004\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"509004\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468465776\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{13}{20}},0.61,{\\Large\\frac{11}{16}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the fractions to decimals.<\/td>\r\n<td>[latex]0.65,0.61,0.6875[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the smallest decimal number first.<\/td>\r\n<td>[latex]0.61[\/latex] , _____ , _____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the next larger decimal number in the middle place.<\/td>\r\n<td>[latex]0.61,0.65[\/latex] , _____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the last decimal number (the larger) in the third place.<\/td>\r\n<td>[latex]0.61,0.65,0.6875[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the list with the original fractions.<\/td>\r\n<td>[latex]0.61,{\\Large\\frac{13}{20}},{\\Large\\frac{11}{16}}[\/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]146294[\/ohm_question]\r\n\r\n<\/div>\r\nTo see more examples, watch this video example.\r\n\r\nhttps:\/\/youtu.be\/f4theaYuVuo","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Order fractions and decimals by writing fractions as decimals<\/li>\n<\/ul>\n<\/div>\n<h2>Order Decimals and Fractions<\/h2>\n<p>In and 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}}) (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}}) (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) (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<p>&nbsp;<\/p>\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<p>When ordering negative numbers, remember that larger numbers are to the right on the number line and any positive number is greater than any negative number.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Order [latex](-0.5) (-{\\Large\\frac{3}{4}})[\/latex] using [latex]&lt[\/latex]; or [latex]\\text{>.}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q677046\">Show Solution<\/span><\/p>\n<div id=\"q677046\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466186266\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex](-0.5) (-{\\Large\\frac{3}{4}})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]-{\\Large\\frac{3}{4}}[\/latex] to a decimal.<\/td>\n<td>[latex](-0.5) (- 0.75)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Compare [latex]-0.5[\/latex] to [latex]-0.75[\/latex] .<\/td>\n<td>[latex]-0.5>-0.75[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the inequality with the original fraction.<\/td>\n<td>[latex]-0.5>-{\\Large\\frac{3}{4}}[\/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=\"ohm146290\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146290&theme=oea&iframe_resize_id=ohm146290&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>Write the numbers [latex]{\\Large\\frac{13}{20}},0.61,{\\Large\\frac{11}{16}}[\/latex] in order from smallest to largest.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q509004\">Show Solution<\/span><\/p>\n<div id=\"q509004\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468465776\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{13}{20}},0.61,{\\Large\\frac{11}{16}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert the fractions to decimals.<\/td>\n<td>[latex]0.65,0.61,0.6875[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write the smallest decimal number first.<\/td>\n<td>[latex]0.61[\/latex] , _____ , _____<\/td>\n<\/tr>\n<tr>\n<td>Write the next larger decimal number in the middle place.<\/td>\n<td>[latex]0.61,0.65[\/latex] , _____<\/td>\n<\/tr>\n<tr>\n<td>Write the last decimal number (the larger) in the third place.<\/td>\n<td>[latex]0.61,0.65,0.6875[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the list with the original fractions.<\/td>\n<td>[latex]0.61,{\\Large\\frac{13}{20}},{\\Large\\frac{11}{16}}[\/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=\"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>To see more examples, watch this video example.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" 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\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-3929\">\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 146286, 146290, 146294. <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>Ex: Order Fractions and Decimals From Least to Greatest. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <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 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":12,"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\":\"Ex: Order Fractions and Decimals From Least to Greatest\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/f4theaYuVuo\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146286, 146290, 146294\",\"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-3929","chapter","type-chapter","status-web-only","hentry"],"part":377,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3929","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\/3929\/revisions"}],"predecessor-version":[{"id":3930,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3929\/revisions\/3930"}],"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\/3929\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3929"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3929"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3929"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}