{"id":229363,"date":"2025-06-08T06:36:00","date_gmt":"2025-06-08T06:36:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229363"},"modified":"2025-06-08T06:36:02","modified_gmt":"2025-06-08T06:36:02","slug":"what-is-0-8-repeating-as-a-fraction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/what-is-0-8-repeating-as-a-fraction\/","title":{"rendered":"What is 0.8 repeating as a fraction"},"content":{"rendered":"\n

What is 0.8 repeating as a fraction<\/p>\n\n\n\n

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

ChatGPT said:<\/h6>\n\n\n\n

Correct Answer:<\/h3>\n\n\n\n

The decimal 0.8 repeating<\/strong> (written as 0.8\u203e0.\\overline{8}0.8) is equal to the fraction 89\\frac{8}{9}98\u200b<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

To understand why 0.8\u203e=890.\\overline{8} = \\frac{8}{9}0.8=98\u200b, we need to explore how repeating decimals convert into fractions.<\/p>\n\n\n\n

Step-by-Step Conversion:<\/h4>\n\n\n\n
    \n
  1. Let x=0.8\u203ex = 0.\\overline{8}x=0.8, which means the digit 8 repeats forever:
    x=0.88888\u2026x = 0.88888\\ldotsx=0.88888\u2026<\/li>\n\n\n\n
  2. Multiply both sides by 10 to move the decimal point one place to the right:
    10x=8.88888\u202610x = 8.88888\\ldots10x=8.88888\u2026<\/li>\n\n\n\n
  3. Now subtract the original equation from this new equation: 10x=8.88888\u2026\u2212x=0.88888\u20269x=8\\begin{align*} 10x &= 8.88888\\ldots \\\\ – x &= 0.88888\\ldots \\\\ \\hline 9x &= 8 \\end{align*}10x\u2212x9x\u200b=8.88888\u2026=0.88888\u2026=8\u200b\u200b<\/li>\n\n\n\n
  4. Solve for xxx:
    x=89x = \\frac{8}{9}x=98\u200b<\/li>\n<\/ol>\n\n\n\n

    This shows that the repeating decimal 0.8\u203e0.\\overline{8}0.8 is exactly equal to 89\\frac{8}{9}98\u200b.<\/p>\n\n\n\n

    \n\n\n\n

    Why This Works:<\/h4>\n\n\n\n

    Repeating decimals have patterns that make them expressible as fractions. When a decimal repeats, multiplying by a power of 10 helps align the repeating digits. Subtracting removes the repeating part, leaving a solvable equation.<\/p>\n\n\n\n

    The method works for any single-digit repeating decimal:<\/p>\n\n\n\n

      \n
    • 0.1\u203e=190.\\overline{1} = \\frac{1}{9}0.1=91\u200b<\/li>\n\n\n\n
    • 0.2\u203e=290.\\overline{2} = \\frac{2}{9}0.2=92\u200b<\/li>\n\n\n\n
    • \u2026<\/li>\n\n\n\n
    • 0.8\u203e=890.\\overline{8} = \\frac{8}{9}0.8=98\u200b<\/li>\n\n\n\n
    • 0.9\u203e=99=10.\\overline{9} = \\frac{9}{9} = 10.9=99\u200b=1<\/li>\n<\/ul>\n\n\n\n

      This pattern reveals that repeating decimals represent rational numbers\u2014numbers that can be written as ratios of integers.<\/p>\n\n\n\n

      \n\n\n\n

      Final Note:<\/h4>\n\n\n\n

      Understanding how repeating decimals become fractions helps clarify the nature of rational numbers and shows that what looks like an endless decimal is actually a precise, finite value in fractional form. So, 0.8\u203e=890.\\overline{8} = \\frac{8}{9}0.8=98\u200b<\/strong> is exact and not an approximation.<\/p>\n\n\n\n

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

      What is 0.8 repeating as a fraction The Correct Answer and Explanation is: ChatGPT said: Correct Answer: The decimal 0.8 repeating (written as 0.8\u203e0.\\overline{8}0.8) is equal to the fraction 89\\frac{8}{9}98\u200b. Explanation To understand why 0.8\u203e=890.\\overline{8} = \\frac{8}{9}0.8=98\u200b, we need to explore how repeating decimals convert into fractions. Step-by-Step Conversion: This shows that the repeating decimal […]<\/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-229363","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229363","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=229363"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229363\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}