{"id":155621,"date":"2024-10-16T08:31:50","date_gmt":"2024-10-16T08:31:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=155621"},"modified":"2024-10-16T08:33:00","modified_gmt":"2024-10-16T08:33:00","slug":"what-is-1-21-repeating-as-a-fraction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/16\/what-is-1-21-repeating-as-a-fraction\/","title":{"rendered":"What is 1.21 repeating as a fraction"},"content":{"rendered":"\n<p>What is 1.21 repeating as a fraction?<\/p>\n\n\n\n<p>The correct answer is: <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-3-color\"><strong>(\\frac{40}{33})<\/strong><\/mark><\/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>To express the repeating decimal (1.21\\overline{21}) as a fraction, we can use a method that involves setting up an equation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define the Decimal<\/h3>\n\n\n\n<p>Let:<br>[<br>x = 1.212121\\ldots<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Multiply by a Power of 10<\/h3>\n\n\n\n<p>To eliminate the repeating part, we multiply (x) by (100) (because the repeating part consists of two digits):<br>[<br>100x = 121.212121\\ldots<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Set Up the Equation<\/h3>\n\n\n\n<p>Now we have two equations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(x = 1.212121\\ldots)<\/li>\n\n\n\n<li>(100x = 121.212121\\ldots)<\/li>\n<\/ol>\n\n\n\n<p>Next, we subtract the first equation from the second:<br>[<br>100x &#8211; x = 121.212121\\ldots &#8211; 1.212121\\ldots<br>]<br>This simplifies to:<br>[<br>99x = 120<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for (x)<\/h3>\n\n\n\n<p>Now, solve for (x) by dividing both sides by (99):<br>[<br>x = \\frac{120}{99}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Simplify the Fraction<\/h3>\n\n\n\n<p>To simplify (\\frac{120}{99}), we need to find the greatest common divisor (GCD) of (120) and (99).<\/p>\n\n\n\n<p>The GCD can be found using the Euclidean algorithm:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(120) divided by (99) gives a remainder of (21).<\/li>\n\n\n\n<li>(99) divided by (21) gives a remainder of (15).<\/li>\n\n\n\n<li>(21) divided by (15) gives a remainder of (6).<\/li>\n\n\n\n<li>(15) divided by (6) gives a remainder of (3).<\/li>\n\n\n\n<li>(6) divided by (3) gives a remainder of (0).<\/li>\n<\/ul>\n\n\n\n<p>Thus, the GCD is (3). Now, divide both the numerator and denominator by their GCD:<br>[<br>\\frac{120 \\div 3}{99 \\div 3} = \\frac{40}{33}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>So, the repeating decimal (1.21\\overline{21}) as a fraction is:<br>[<br>\\frac{40}{33}<br>]<\/p>\n\n\n\n<p>This fraction cannot be simplified further, as (40) and (33) have no common factors other than (1). Thus, the final result is (\\frac{40}{33}).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is 1.21 repeating as a fraction? The correct answer is: (\\frac{40}{33}) The Correct Answer and Explanation is : To express the repeating decimal (1.21\\overline{21}) as a fraction, we can use a method that involves setting up an equation. Step 1: Define the Decimal Let:[x = 1.212121\\ldots] Step 2: Multiply by a Power of 10 [&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-155621","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155621","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=155621"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/155621\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=155621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=155621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=155621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}