{"id":249839,"date":"2025-07-10T05:39:04","date_gmt":"2025-07-10T05:39:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249839"},"modified":"2025-07-10T05:39:09","modified_gmt":"2025-07-10T05:39:09","slug":"decimal-representation-of-rational-number-827-is","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/decimal-representation-of-rational-number-827-is\/","title":{"rendered":"Decimal representation of rational number 8\\27 is"},"content":{"rendered":"\n<p>5\\ 6 in the decimal form is:\\ (a) 0.8\\bar{3} (b) 0.8\\bar{33} (c) 0.6\\bar{3} (d) 0.6\\bar{33}\\ Decimal representation of rational number 8\\27 is:\\ (a) 0.\\bar{296} (b) 0.2\\bar{96} (c) 0.29\\bar{6} (d) 0.296<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s break these two problems down step by step:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Decimal Representation of 5\/6<\/h3>\n\n\n\n<p>To convert 5\/6 into decimal form, we perform long division:<\/p>\n\n\n\n<p><strong>5 \u00f7 6<\/strong> gives:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 goes into 50 eight times (6 \u00d7 8 = 48).<\/li>\n\n\n\n<li>Subtract 50 &#8211; 48 = 2.<\/li>\n\n\n\n<li>Bring down a zero, making it 20.<\/li>\n\n\n\n<li>6 goes into 20 three times (6 \u00d7 3 = 18).<\/li>\n\n\n\n<li>Subtract 20 &#8211; 18 = 2.<\/li>\n\n\n\n<li>Notice the remainder repeats as 2.<\/li>\n<\/ul>\n\n\n\n<p>The repeating part is &#8220;3&#8221;, so the decimal form of 5\/6 is <strong>0.83 repeating<\/strong>, or <strong>0.8\u03053<\/strong>.<\/p>\n\n\n\n<p>Therefore, the correct answer is <strong>(a) 0.8\u03053<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Decimal Representation of 8\/27<\/h3>\n\n\n\n<p>Next, let&#8217;s convert 8\/27 into decimal form using long division:<\/p>\n\n\n\n<p><strong>8 \u00f7 27<\/strong> gives:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>27 goes into 80 two times (27 \u00d7 2 = 54).<\/li>\n\n\n\n<li>Subtract 80 &#8211; 54 = 26.<\/li>\n\n\n\n<li>Bring down a zero, making it 260.<\/li>\n\n\n\n<li>27 goes into 260 nine times (27 \u00d7 9 = 243).<\/li>\n\n\n\n<li>Subtract 260 &#8211; 243 = 17.<\/li>\n\n\n\n<li>Bring down another zero, making it 170.<\/li>\n\n\n\n<li>27 goes into 170 six times (27 \u00d7 6 = 162).<\/li>\n\n\n\n<li>Subtract 170 &#8211; 162 = 8, which repeats.<\/li>\n<\/ul>\n\n\n\n<p>The repeating part is &#8220;296&#8221;, so the decimal form of 8\/27 is <strong>0.296\u0305<\/strong>.<\/p>\n\n\n\n<p>Therefore, the correct answer is <strong>(a) 0.\u0305296<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The decimal form of <strong>5\/6<\/strong> is <strong>0.8\u03053<\/strong>, and the correct answer is <strong>(a)<\/strong>.<\/li>\n\n\n\n<li>The decimal form of <strong>8\/27<\/strong> is <strong>0.\u0305296<\/strong>, and the correct answer is <strong>(a)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-7.jpeg\" alt=\"\" class=\"wp-image-249840\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>5\\ 6 in the decimal form is:\\ (a) 0.8\\bar{3} (b) 0.8\\bar{33} (c) 0.6\\bar{3} (d) 0.6\\bar{33}\\ Decimal representation of rational number 8\\27 is:\\ (a) 0.\\bar{296} (b) 0.2\\bar{96} (c) 0.29\\bar{6} (d) 0.296 The Correct Answer and Explanation is: Let&#8217;s break these two problems down step by step: 1. Decimal Representation of 5\/6 To convert 5\/6 into decimal [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-249839","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=249839"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249839\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}