{"id":252779,"date":"2025-07-11T12:22:24","date_gmt":"2025-07-11T12:22:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252779"},"modified":"2025-07-11T12:22:26","modified_gmt":"2025-07-11T12:22:26","slug":"which-of-the-following-are-terminating-decimals","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/which-of-the-following-are-terminating-decimals\/","title":{"rendered":"which of the following are terminating decimals"},"content":{"rendered":"\n<p>which of the following are terminating decimals 1)5\/7 2)11\/20 3)5\/4 4)31\/60<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answers are:<\/p>\n\n\n\n<p><strong>2) 11\/20 and 3) 5\/4 are terminating decimals.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To determine if a fraction has a terminating decimal, you need to look at its <strong>denominator<\/strong> (after simplifying the fraction). A <strong>terminating decimal<\/strong> is a decimal that ends after a certain number of digits. For a fraction to terminate, the only <strong>prime factors<\/strong> of its denominator (after simplification) must be <strong>2 and\/or 5<\/strong>. These are the prime factors of 10, the base of our number system.<\/p>\n\n\n\n<p>Let\u2019s analyze each fraction:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>1) 5\/7<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Denominator = 7<\/li>\n\n\n\n<li>Prime factor: 7<\/li>\n\n\n\n<li>Since 7 is not 2 or 5, this fraction does <strong>not<\/strong> have a terminating decimal.<\/li>\n\n\n\n<li>Decimal form: 0.714285&#8230; (repeats)<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion: Not terminating<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>2) 11\/20<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Denominator = 20<\/li>\n\n\n\n<li>Prime factorization: 20 = 2\u00b2 \u00d7 5<\/li>\n\n\n\n<li>All prime factors are 2 and 5.<\/li>\n\n\n\n<li>Decimal form: 0.55<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion: Terminating<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>3) 5\/4<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Denominator = 4<\/li>\n\n\n\n<li>Prime factorization: 4 = 2\u00b2<\/li>\n\n\n\n<li>Only prime factor is 2<\/li>\n\n\n\n<li>Decimal form: 1.25<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion: Terminating<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>4) 31\/60<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Denominator = 60<\/li>\n\n\n\n<li>Prime factorization: 60 = 2\u00b2 \u00d7 3 \u00d7 5<\/li>\n\n\n\n<li>Contains 3, which is not allowed<\/li>\n\n\n\n<li>Decimal form: 0.51666&#8230; (repeats)<\/li>\n<\/ul>\n\n\n\n<p><strong>Conclusion: Not terminating<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>11\/20 and 5\/4 are terminating decimals<\/strong><br><strong>5\/7 and 31\/60 are not terminating decimals<\/strong> because their denominators include prime factors other than 2 or 5.<\/p>\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-banner6-269.jpeg\" alt=\"\" class=\"wp-image-252788\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>which of the following are terminating decimals 1)5\/7 2)11\/20 3)5\/4 4)31\/60 The Correct Answer and Explanation is: The correct answers are: 2) 11\/20 and 3) 5\/4 are terminating decimals. Explanation: To determine if a fraction has a terminating decimal, you need to look at its denominator (after simplifying the fraction). A terminating decimal is a [&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-252779","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252779","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=252779"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252779\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}