{"id":227926,"date":"2025-06-06T15:25:12","date_gmt":"2025-06-06T15:25:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227926"},"modified":"2025-06-06T15:25:14","modified_gmt":"2025-06-06T15:25:14","slug":"convert-3-5-in-to-a-fraction-with-5-repeating","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/convert-3-5-in-to-a-fraction-with-5-repeating\/","title":{"rendered":"convert 3.5 in to a fraction with 5 repeating"},"content":{"rendered":"\n<p>convert 3.5 in to a fraction with 5 repeating<\/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<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>The decimal <strong>3.5 with 5 repeating<\/strong> means:<br><strong>3.55555\u2026<\/strong> (i.e., 5 repeats infinitely).<\/p>\n\n\n\n<p>This is a <strong>repeating decimal<\/strong>, and we can convert it to a fraction as follows:<\/p>\n\n\n\n<p>Let:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>x = 3.55555\u2026<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>Step 1: Multiply both sides by 10 to shift the decimal point one place:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>10x = 35.55555\u2026<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>Step 2: Subtract the original equation from this new equation:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>10x &#8211; x = 35.55555\u2026 &#8211; 3.55555\u2026<\/strong><br><strong>9x = 32<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>Step 3: Solve for x:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>x = 32 \/ 9<\/strong><\/p>\n<\/blockquote>\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<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>3.5 with 5 repeating = 32\/9<\/strong><\/p>\n<\/blockquote>\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>Repeating decimals can be converted to fractions using algebraic techniques. The repeating decimal in question is <strong>3.55555\u2026<\/strong>, where only the digit &#8220;5&#8221; repeats endlessly. To convert it into a fraction, we begin by setting the decimal equal to a variable, say xxx, so that x=3.5555\u2026x = 3.5555\\ldotsx=3.5555\u2026.<\/p>\n\n\n\n<p>The repeating part is only one digit long, so we multiply both sides by 10 to shift the decimal one place to the right, which gives us 10x=35.5555\u202610x = 35.5555\\ldots10x=35.5555\u2026. The key idea here is to eliminate the repeating decimal part by subtraction. We subtract the original equation x=3.5555\u2026x = 3.5555\\ldotsx=3.5555\u2026 from the new one: 10x\u2212x=35.5555\u2026\u22123.5555\u202610x &#8211; x = 35.5555\\ldots &#8211; 3.5555\\ldots10x\u2212x=35.5555\u2026\u22123.5555\u2026 9x=329x = 329x=32<\/p>\n\n\n\n<p>When we subtract, the infinite decimals cancel out because they are the same after the decimal point. We\u2019re left with a solvable linear equation: 9x=329x = 329x=32. Solving for xxx, we get x=329x = \\frac{32}{9}x=932\u200b. This fraction is already in its simplest form because 32 and 9 have no common factors other than 1.<\/p>\n\n\n\n<p>This method works reliably for any repeating decimal, and it shows the close relationship between repeating decimals and rational numbers. Every repeating decimal can be expressed as a fraction, which means it\u2019s a rational number. So, 3.5\u203e=3293.\\overline{5} = \\frac{32}{9}3.5=932\u200b is a rational expression of that repeating decimal.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-546.jpeg\" alt=\"\" class=\"wp-image-227927\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>convert 3.5 in to a fraction with 5 repeating The Correct Answer and Explanation is: Correct Answer: The decimal 3.5 with 5 repeating means:3.55555\u2026 (i.e., 5 repeats infinitely). This is a repeating decimal, and we can convert it to a fraction as follows: Let: x = 3.55555\u2026 Step 1: Multiply both sides by 10 to [&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-227926","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227926","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=227926"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227926\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227926"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227926"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}