To convert the decimal 0.16 repeating (written as 0.166666… where the 6 repeats) into a fraction, we can follow a step-by-step process.<\/p>\n\n\n\n
Step 1: Set up an equation<\/h3>\n\n\n\n
Let x=0.166666… x = 0.166666…x=0.166666…, where the 6 repeats indefinitely. Now, multiply both sides of the equation by 10 to shift the decimal point one place to the right:10x=1.666666…10x = 1.666666…10x=1.666666…<\/p>\n\n\n\n
Step 2: Subtract the original equation from the new equation<\/h3>\n\n\n\n
Now subtract the original equation from this new one:10x\u2212x=1.666666…\u22120.166666…10x – x = 1.666666… – 0.166666…10x\u2212x=1.666666…\u22120.166666…<\/p>\n\n\n\n
Simplifying both sides:9x=1.59x = 1.59x=1.5<\/p>\n\n\n\n
Step 3: Solve for xxx<\/h3>\n\n\n\n
Now, divide both sides of the equation by 9:x=1.59x = \\frac{1.5}{9}x=91.5\u200b<\/p>\n\n\n\n
To eliminate the decimal, multiply both the numerator and denominator by 10:x=1590x = \\frac{15}{90}x=9015\u200b<\/p>\n\n\n\n
Step 4: Simplify the fraction<\/h3>\n\n\n\n
Now simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15:x=15\u00f71590\u00f715=16x = \\frac{15 \\div 15}{90 \\div 15} = \\frac{1}{6}x=90\u00f71515\u00f715\u200b=61\u200b<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
Thus, 0.166\u203e0.16 \\overline{6}0.166 as a fraction is 16\\frac{1}{6}61\u200b.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The repeating decimal 0.16 repeating is essentially equivalent to the fraction 16\\frac{1}{6}61\u200b. This method works for any repeating decimal by setting up an equation and then using subtraction and simplification to convert it into a fraction. Repeating decimals are a common occurrence in real numbers, and they can often be converted into fractions for easier calculation or representation.<\/p>\n\n\n\n what is 0.16, 6 repeating as a fraction? The Correct Answer and Explanation is: To convert the decimal 0.16 repeating (written as 0.166666… where the 6 repeats) into a fraction, we can follow a step-by-step process. Step 1: Set up an equation Let x=0.166666… x = 0.166666…x=0.166666…, where the 6 repeats indefinitely. Now, multiply both […]<\/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-240909","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240909","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=240909"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240909\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-145.jpeg\")
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