{"id":146236,"date":"2024-09-30T13:55:36","date_gmt":"2024-09-30T13:55:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146236"},"modified":"2024-09-30T13:55:39","modified_gmt":"2024-09-30T13:55:39","slug":"which-fraction-has-a-repeating-decimal-as-its-decimal-expansion","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/which-fraction-has-a-repeating-decimal-as-its-decimal-expansion\/","title":{"rendered":"Which fraction has a repeating decimal as its decimal expansion"},"content":{"rendered":"\n<p>Which fraction has a repeating decimal as its decimal expansion?<br>3\/25<br>3\/16<br>3\/11<br>3\/8<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Among the given fractions, the one with a repeating decimal expansion is <strong>3\/11<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Decimal Expansions of Fractions:<\/h4>\n\n\n\n<p>When dividing two integers to convert a fraction into a decimal, you can either get a terminating or a repeating decimal. A terminating decimal occurs when the division results in a finite number of digits after the decimal point. A repeating decimal, on the other hand, occurs when the decimal digits continue infinitely in a repeating pattern.<\/p>\n\n\n\n<p>The type of decimal expansion depends on the denominator of the fraction when it is in its simplest form. Specifically:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>terminating decimal<\/strong> occurs when the denominator, after removing any common factors with the numerator, has only the prime factors 2 or 5. This is because powers of 2 or 5 divide evenly into powers of 10, which makes the division terminate.<\/li>\n\n\n\n<li>A <strong>repeating decimal<\/strong> occurs when the denominator has prime factors other than 2 or 5, as these do not divide evenly into powers of 10. As a result, the decimal repeats.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Check each fraction:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>3\/25<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>25 = 5\u00b2 (denominator has only the prime factor 5).<\/li>\n\n\n\n<li>Decimal expansion is terminating: 3 \u00f7 25 = 0.12.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>3\/16<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>16 = 2\u2074 (denominator has only the prime factor 2).<\/li>\n\n\n\n<li>Decimal expansion is terminating: 3 \u00f7 16 = 0.1875.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>3\/11<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>11 is a prime number and does not divide powers of 10 evenly.<\/li>\n\n\n\n<li>Decimal expansion is repeating: 3 \u00f7 11 = 0.272727\u2026, with &#8220;27&#8221; repeating.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>3\/8<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8 = 2\u00b3 (denominator has only the prime factor 2).<\/li>\n\n\n\n<li>Decimal expansion is terminating: 3 \u00f7 8 = 0.375.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Conclusion:<\/h4>\n\n\n\n<p>The fraction <strong>3\/11<\/strong> has a repeating decimal because its denominator contains a prime factor (11) other than 2 or 5, resulting in the repeating decimal 0.272727\u2026<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which fraction has a repeating decimal as its decimal expansion?3\/253\/163\/113\/8 The Correct Answer and Explanation is : Among the given fractions, the one with a repeating decimal expansion is 3\/11. Explanation: Decimal Expansions of Fractions: When dividing two integers to convert a fraction into a decimal, you can either get a terminating or a repeating [&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-146236","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146236","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=146236"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146236\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}