{"id":185653,"date":"2025-01-22T19:50:17","date_gmt":"2025-01-22T19:50:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185653"},"modified":"2025-01-22T19:50:18","modified_gmt":"2025-01-22T19:50:18","slug":"express-the-repeating-decimal-as-a-fraction-in-lowest-terms","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/express-the-repeating-decimal-as-a-fraction-in-lowest-terms\/","title":{"rendered":"Express the repeating decimal as a fraction in lowest terms"},"content":{"rendered":"\n

Express the repeating decimal as a fraction in lowest terms. 83 83 83 0.83 = + + 100 10,000 1,000,000 0.83= (Type an integer or a simplified fraction.)<\/p>\n\n\n\n

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

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

To convert the repeating decimal (0.\\overline{83}) into a fraction, we follow the steps outlined below.<\/p>\n\n\n\n

Step 1: Let (x = 0.\\overline{83})<\/h3>\n\n\n\n

This means that (x = 0.838383\u2026), where “83” repeats indefinitely.<\/p>\n\n\n\n

Step 2: Eliminate the repeating decimal<\/h3>\n\n\n\n

To eliminate the repeating part, multiply both sides of the equation by 100. This shifts the decimal point two places to the right:<\/p>\n\n\n\n

[
100x = 83.838383\u2026
]<\/p>\n\n\n\n

Now we have:<\/p>\n\n\n\n

    \n
  • (x = 0.838383\u2026)<\/li>\n\n\n\n
  • (100x = 83.838383\u2026)<\/li>\n<\/ul>\n\n\n\n

    Step 3: Subtract the two equations<\/h3>\n\n\n\n

    Subtract the first equation ((x = 0.838383\u2026)) from the second equation ((100x = 83.838383\u2026)):<\/p>\n\n\n\n

    [
    100x – x = 83.838383\u2026 – 0.838383\u2026
    ]<\/p>\n\n\n\n

    Simplifying:<\/p>\n\n\n\n

    [
    99x = 83
    ]<\/p>\n\n\n\n

    Step 4: Solve for (x)<\/h3>\n\n\n\n

    Now, solve for (x) by dividing both sides of the equation by 99:<\/p>\n\n\n\n

    [
    x = \\frac{83}{99}
    ]<\/p>\n\n\n\n

    Step 5: Simplify the fraction<\/h3>\n\n\n\n

    The fraction (\\frac{83}{99}) is in its lowest terms because 83 is a prime number, and it does not divide 99. Therefore, (\\frac{83}{99}) is the simplest form of the fraction.<\/p>\n\n\n\n

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

    [
    0.\\overline{83} = \\frac{83}{99}
    ]<\/p>\n\n\n\n

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

    To summarize, by using the method of subtracting equations and multiplying by a power of 10, we were able to express the repeating decimal (0.\\overline{83}) as a fraction. This process is a common approach for converting repeating decimals into fractions. We ended up with the fraction (\\frac{83}{99}), which is in its lowest terms.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Express the repeating decimal as a fraction in lowest terms. 83 83 83 0.83 = + + 100 10,000 1,000,000 0.83= (Type an integer or a simplified fraction.) The Correct Answer and Explanation is : To convert the repeating decimal (0.\\overline{83}) into a fraction, we follow the steps outlined below. Step 1: Let (x = […]<\/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-185653","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185653","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=185653"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185653\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185653"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185653"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}