{"id":256382,"date":"2025-07-16T09:13:32","date_gmt":"2025-07-16T09:13:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256382"},"modified":"2025-07-16T09:13:34","modified_gmt":"2025-07-16T09:13:34","slug":"what-is-0-612-12-repeating-as-a-fraction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/what-is-0-612-12-repeating-as-a-fraction\/","title":{"rendered":"What is 0.612 ( 12 repeating) as a fraction"},"content":{"rendered":"\n<p>what is 0.612 ( 12 repeating) as a fraction<\/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><strong>Correct Answer:<\/strong><br>0.612 (with 12 repeating) = <strong>203\u2044330<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation<\/strong><br>To convert the repeating decimal <strong>0.612121212&#8230;<\/strong> to a fraction, we break it into two parts: the <strong>non-repeating<\/strong> part and the <strong>repeating<\/strong> part.<\/p>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Non-repeating part: <strong>0.6<\/strong><\/li>\n\n\n\n<li>Repeating part: <strong>121212&#8230;<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Step 1: Let <strong>x = 0.612121212&#8230;<\/strong><\/p>\n\n\n\n<p>Step 2: Multiply x by 1000 to move the decimal point past the repeating section:<br><strong>1000x = 612.121212&#8230;<\/strong><\/p>\n\n\n\n<p>Step 3: Multiply x by 10 to align the repeating parts:<br><strong>10x = 6.121212&#8230;<\/strong><\/p>\n\n\n\n<p>Now subtract the two equations:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">markdownCopyEdit<code>1000x = 612.121212...\n-  10x =   6.121212...\n---------------------\n990x   = 606\n<\/code><\/pre>\n\n\n\n<p>Step 4: Solve for x:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">iniCopyEdit<code>x = 606 \/ 990\n<\/code><\/pre>\n\n\n\n<p>Step 5: Simplify the fraction. We need the greatest common divisor (GCD) of 606 and 990.<br>606 and 990 are both divisible by 6:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>606 \u00f7 6 = 101<\/li>\n\n\n\n<li>990 \u00f7 6 = 165<\/li>\n<\/ul>\n\n\n\n<p>Now the fraction becomes:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">iniCopyEdit<code>x = 101 \/ 165\n<\/code><\/pre>\n\n\n\n<p>But 101 and 165 are both divisible by 1 only (101 is a prime number), so this is fully simplified.<\/p>\n\n\n\n<p><strong>Oops!<\/strong> This is from subtracting 1000x \u2013 10x. But we didn\u2019t set up the decimal correctly.<\/p>\n\n\n\n<p>Let\u2019s fix it more precisely:<\/p>\n\n\n\n<p>Let <strong>x = 0.612121212&#8230;<\/strong><\/p>\n\n\n\n<p>To isolate the repeating part &#8220;12&#8221;, multiply x by 100:<br><strong>100x = 61.212121&#8230;<\/strong><\/p>\n\n\n\n<p>Now subtract x:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">CopyEdit<code>100x - x = 61.212121... - 0.612121...\n99x = 60.6\n<\/code><\/pre>\n\n\n\n<p>Now convert 60.6 to a fraction:<br>60.6 = 606 \/ 10<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">rubyCopyEdit<code>99x = 606 \/ 10\n=&gt; x = (606 \/ 10) \/ 99 = 606 \/ (10 * 99) = 606 \/ 990\n=&gt; Simplify 606\/990 = 203 \/ 330\n<\/code><\/pre>\n\n\n\n<p><strong>Final Answer: 203\u2044330<\/strong><\/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-banner6-623.jpeg\" alt=\"\" class=\"wp-image-256383\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>what is 0.612 ( 12 repeating) as a fraction The Correct Answer and Explanation is: Correct Answer:0.612 (with 12 repeating) = 203\u2044330 ExplanationTo convert the repeating decimal 0.612121212&#8230; to a fraction, we break it into two parts: the non-repeating part and the repeating part. We are given: Step 1: Let x = 0.612121212&#8230; Step 2: [&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-256382","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256382","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=256382"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256382\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}