To express the repeating decimal 6.3 repeating as a fraction, we need to use algebra to solve for the value.<\/p>\n\n\n\n
Step 1: Represent the decimal as a variable<\/h3>\n\n\n\n
Let xxx represent the repeating decimal:x=6.33333\u2026x = 6.33333\\ldotsx=6.33333\u2026<\/p>\n\n\n\n
Here, the digit “3” repeats indefinitely.<\/p>\n\n\n\n
Step 2: Eliminate the repeating decimal<\/h3>\n\n\n\n
To isolate the repeating part, multiply both sides of the equation by 10, since the repeating digit “3” starts immediately after the decimal point:10x=63.33333\u202610x = 63.33333\\ldots10x=63.33333\u2026<\/p>\n\n\n\n
Now, we have two equations:<\/p>\n\n\n\n
- \n
- x=6.33333\u2026x = 6.33333\\ldotsx=6.33333\u2026<\/li>\n\n\n\n
- 10x=63.33333\u202610x = 63.33333\\ldots10x=63.33333\u2026<\/li>\n<\/ol>\n\n\n\n
Step 3: Subtract the first equation from the second<\/h3>\n\n\n\n
To eliminate the repeating decimal, subtract equation (1) from equation (2):10x\u2212x=63.33333\u2026\u22126.33333\u202610x – x = 63.33333\\ldots – 6.33333\\ldots10x\u2212x=63.33333\u2026\u22126.33333\u2026<\/p>\n\n\n\n
This simplifies to:9x=579x = 579x=57<\/p>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
Now, divide both sides of the equation by 9:x=579x = \\frac{57}{9}x=957\u200b<\/p>\n\n\n\n
Step 5: Simplify the fraction<\/h3>\n\n\n\n
The fraction 579\\frac{57}{9}957\u200b can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:x=57\u00f739\u00f73=193x = \\frac{57 \\div 3}{9 \\div 3} = \\frac{19}{3}x=9\u00f7357\u00f73\u200b=319\u200b<\/p>\n\n\n\n
Final Answer<\/h3>\n\n\n\n
Therefore, the repeating decimal 6.3 repeating can be expressed as the fraction 193\\frac{19}{3}319\u200b.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The method we used to convert the repeating decimal into a fraction is based on algebraic manipulation. By multiplying the equation by 10, we shift the decimal point, and subtracting allows us to isolate the repeating portion. Once the equation is simplified, we solve for the fraction and simplify it to its lowest terms. This method is applicable to any repeating decimal, whether it’s a single digit or multiple digits repeating.<\/p>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"what is 6.3 repeating as a fraction The Correct Answer and Explanation is: To express the repeating decimal 6.3 repeating as a fraction, we need to use algebra to solve for the value. Step 1: Represent the decimal as a variable Let xxx represent the repeating decimal:x=6.33333\u2026x = 6.33333\\ldotsx=6.33333\u2026 Here, the digit “3” repeats indefinitely. […]<\/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-258912","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258912","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=258912"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258912\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258912"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258912"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}