{"id":227088,"date":"2025-06-05T19:21:49","date_gmt":"2025-06-05T19:21:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227088"},"modified":"2025-06-05T19:21:51","modified_gmt":"2025-06-05T19:21:51","slug":"how-is-0-24overline6-written-as-a-fraction-in-simplest-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/how-is-0-24overline6-written-as-a-fraction-in-simplest-form\/","title":{"rendered":"How is 0.24\\overline{6} written as a fraction in simplest form"},"content":{"rendered":"\n

How is 0.24\\overline{6} written as a fraction in simplest form?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Step-by-Step Conversion:<\/strong><\/h3>\n\n\n\n

Let
x=0.246666\u2026x = 0.246666\\ldotsx=0.246666\u2026<\/p>\n\n\n\n

Split it into non-repeating and repeating parts:<\/p>\n\n\n\n

    \n
  1. Let\u2019s isolate the repeating part:\n
      \n
    • Multiply by 10 to move past the non-repeating 2 digits: 10x=2.46666\u202610x = 2.46666\\ldots10x=2.46666\u2026<\/li>\n\n\n\n
    • Multiply by 1000 to move past the repeating digit: 1000x=246.666\u20261000x = 246.666\\ldots1000x=246.666\u2026<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Subtract the two equations: 1000x\u221210x=246.666\u2026\u22122.4666\u20261000x – 10x = 246.666\\ldots – 2.4666\\ldots1000x\u221210x=246.666\u2026\u22122.4666\u2026 990x=244.2990x = 244.2990x=244.2 Now convert 244.2 into a fraction: 244.2=244210244.2 = \\frac{2442}{10}244.2=102442\u200b So, 990x=244210990x = \\frac{2442}{10}990x=102442\u200b Multiply both sides by 10: 9900x=24429900x = 24429900x=2442 x=24429900x = \\frac{2442}{9900}x=99002442\u200b<\/li>\n\n\n\n
    • Simplify the fraction<\/strong>:
      Find the greatest common divisor (GCD) of 2442 and 9900.
      GCD of 2442 and 9900 is 6<\/strong>. 2442\u00f769900\u00f76=4071650\\frac{2442 \\div 6}{9900 \\div 6} = \\frac{407}{1650}9900\u00f762442\u00f76\u200b=1650407\u200b<\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      \u2705 Final Answer:<\/strong><\/h3>\n\n\n\n

      4071650\\boxed{\\frac{407}{1650}}1650407\u200b\u200b<\/p>\n\n\n\n

      \n\n\n\n

      \u270f\ufe0f Explanation<\/strong><\/h3>\n\n\n\n

      To convert the repeating decimal 0.246\u203e0.24\\overline{6}0.246 into a fraction, we need to understand the structure of repeating decimals. This number has two parts: a non-repeating part (\u201c24\u201d) and a repeating part (\u201c6\u201d).<\/p>\n\n\n\n

      We begin by setting the decimal equal to a variable, say x=0.246666\u2026x = 0.246666\\ldotsx=0.246666\u2026. Then we use multiplication to shift the decimal so the repeating digits align. First, multiplying by 10 moves the decimal just past the non-repeating digits, giving us 10x=2.46666\u202610x = 2.46666\\ldots10x=2.46666\u2026. Next, we multiply both sides by 100 to get 1000x=246.666\u20261000x = 246.666\\ldots1000x=246.666\u2026. This allows us to subtract the equations and eliminate the repeating part, resulting in 990x=244.2990x = 244.2990x=244.2.<\/p>\n\n\n\n

      Now, we convert 244.2 to a fraction by recognizing it is 244210\\frac{2442}{10}102442\u200b. So we get: 990x=244210\u21d2x=24429900990x = \\frac{2442}{10} \\Rightarrow x = \\frac{2442}{9900}990x=102442\u200b\u21d2x=99002442\u200b<\/p>\n\n\n\n

      Then we simplify this fraction. The GCD of 2442 and 9900 is 6, so dividing both numerator and denominator by 6 gives 4071650\\frac{407}{1650}1650407\u200b, which is the simplest form.<\/p>\n\n\n\n

      This method is a systematic way to convert any repeating decimal to a fraction using algebra, subtraction, and simplification techniques.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      How is 0.24\\overline{6} written as a fraction in simplest form? The Correct Answer and Explanation is: Step-by-Step Conversion: Letx=0.246666\u2026x = 0.246666\\ldotsx=0.246666\u2026 Split it into non-repeating and repeating parts: \u2705 Final Answer: 4071650\\boxed{\\frac{407}{1650}}1650407\u200b\u200b \u270f\ufe0f Explanation To convert the repeating decimal 0.246\u203e0.24\\overline{6}0.246 into a fraction, we need to understand the structure of repeating decimals. This number has […]<\/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-227088","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227088","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=227088"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227088\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227088"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227088"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}