6.2 recurring as a fraction<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To express (6.2\\overline{6}) (where the digit 6 repeats indefinitely after the decimal point) as a fraction, follow these steps:<\/p>\n\n\n\n Let (x = 6.2\\overline{6}), where the digit 6 repeats.<\/p>\n\n\n\n Since the decimal repeats after the first digit, multiply both sides of the equation by 10 to shift the decimal point one place to the right:<\/p>\n\n\n\n [ Now, subtract the original equation (x = 6.2\\overline{6}) from this new equation:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Now, solve for (x) by dividing both sides of the equation by 9:<\/p>\n\n\n\n [ To simplify (\\frac{56.4}{9}), multiply both the numerator and the denominator by 10 to remove the decimal:<\/p>\n\n\n\n [ Now simplify (\\frac{564}{90}) by finding the greatest common divisor (GCD) of 564 and 90. The GCD is 6, so divide both the numerator and denominator by 6:<\/p>\n\n\n\n [ Thus, (6.2\\overline{6} = \\frac{94}{15}).<\/p>\n\n\n\n The repeating decimal (6.2\\overline{6}) as a fraction is (\\frac{94}{15}).<\/p>\n\n\n\n The key idea in converting repeating decimals to fractions is using algebra to eliminate the repeating portion by shifting the decimal and then solving for the variable. By multiplying the equation by an appropriate power of 10, we align the repeating parts, allowing us to subtract and isolate the repeating part. The fraction can then be simplified by dividing both the numerator and denominator by their greatest common divisor.<\/p>\n","protected":false},"excerpt":{"rendered":" 6.2 recurring as a fraction The Correct Answer and Explanation is: To express (6.2\\overline{6}) (where the digit 6 repeats indefinitely after the decimal point) as a fraction, follow these steps: Step 1: Represent the repeating decimal as a variable Let (x = 6.2\\overline{6}), where the digit 6 repeats. Step 2: Eliminate the repeating decimal Since […]<\/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-167941","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167941","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=167941"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167941\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Represent the repeating decimal as a variable<\/h3>\n\n\n\n
Step 2: Eliminate the repeating decimal<\/h3>\n\n\n\n
10x = 62.6\\overline{6}
]<\/p>\n\n\n\n
10x – x = 62.6\\overline{6} – 6.2\\overline{6}
]<\/p>\n\n\n\n
9x = 56.4
]<\/p>\n\n\n\nStep 3: Solve for (x)<\/h3>\n\n\n\n
x = \\frac{56.4}{9}
]<\/p>\n\n\n\nStep 4: Eliminate the decimal in the numerator<\/h3>\n\n\n\n
x = \\frac{564}{90}
]<\/p>\n\n\n\nStep 5: Simplify the fraction<\/h3>\n\n\n\n
x = \\frac{564 \\div 6}{90 \\div 6} = \\frac{94}{15}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n