{"id":159260,"date":"2024-10-31T14:29:29","date_gmt":"2024-10-31T14:29:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=159260"},"modified":"2024-10-31T14:29:32","modified_gmt":"2024-10-31T14:29:32","slug":"what-is-0-7619047619-as-a-fraction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/31\/what-is-0-7619047619-as-a-fraction\/","title":{"rendered":"What is 0.7619047619 as a fraction"},"content":{"rendered":"\n

What is 0.7619047619 as a fraction?<\/p>\n\n\n\n

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

The decimal 0.7619047619 can be expressed as the fraction ( \\frac{16}{21} ).<\/p>\n\n\n\n

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

To convert a repeating decimal into a fraction, we can use a method that involves algebraic manipulation. Here, the repeating part of 0.7619047619 is “761904,” which repeats indefinitely. This kind of decimal is known as a “repeating decimal.”<\/p>\n\n\n\n

    \n
  1. Set up an equation:<\/strong> Let’s define ( x ) as the repeating decimal: [
    x = 0.7619047619047619 \\ldots
    ]<\/li>\n\n\n\n
  2. Multiply by a power of 10 to align the repeating section:<\/strong> Since “761904” repeats every six digits, we can multiply both sides of the equation by ( 10^6 = 1,000,000 ) to shift the decimal point six places to the right. [
    1,000,000x = 761904.7619047619 \\ldots
    ]<\/li>\n\n\n\n
  3. Set up a second equation for elimination:<\/strong> We also have the original equation ( x = 0.7619047619047619 \\ldots ). Now, we can subtract this equation from the one above to eliminate the repeating decimal part: [
    1,000,000x – x = 761904.7619047619 – 0.7619047619
    ] Simplifying this gives: [
    999,999x = 761904
    ]<\/li>\n\n\n\n
  4. Solve for ( x ):<\/strong> To find the fraction, divide both sides by 999,999: [
    x = \\frac{761904}{999999}
    ]<\/li>\n\n\n\n
  5. Simplify the fraction:<\/strong> The fraction ( \\frac{761904}{999999} ) simplifies to ( \\frac{16}{21} ) by dividing both the numerator and denominator by their greatest common divisor, 47,619.<\/li>\n<\/ol>\n\n\n\n

    Verification:<\/h3>\n\n\n\n

    To confirm, dividing ( 16 ) by ( 21 ) gives approximately 0.7619047619, matching the original decimal. This confirms that the decimal 0.7619047619 is accurately represented by the fraction ( \\frac{16}{21} ).<\/p>\n","protected":false},"excerpt":{"rendered":"

    What is 0.7619047619 as a fraction? The Correct Answer and Explanation is: The decimal 0.7619047619 can be expressed as the fraction ( \\frac{16}{21} ). Explanation: To convert a repeating decimal into a fraction, we can use a method that involves algebraic manipulation. Here, the repeating part of 0.7619047619 is “761904,” which repeats indefinitely. This kind […]<\/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-159260","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159260","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=159260"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159260\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}