The decimal number 0.16666666666\u2026<\/strong> is a repeating decimal<\/strong>, where the digit 6 repeats infinitely<\/strong>. This number can be exactly expressed as the fraction 1\/6<\/strong>.<\/p>\n\n\n\n Decimals that repeat in a consistent pattern can often be written as exact fractions. In this case, the decimal 0.16666666666… (with the 6 repeating forever) is a classic example of a repeating decimal that corresponds to a simple rational number.<\/p>\n\n\n\n Let\u2019s denote the number as:<\/p>\n\n\n\n x = 0.1666666666\u2026<\/strong><\/p>\n\n\n\n We notice the repeating part is just the digit 6<\/strong>, and it starts immediately after the digit 1<\/strong> in the tenths place. Here’s how we can convert this to a fraction step by step.<\/p>\n\n\n\n We want to eliminate the repeating part. To do that, we multiply x by 10 so the repeating part lines up with itself:<\/p>\n\n\n\n 10x = 1.6666666666\u2026<\/strong><\/p>\n\n\n\n Now subtract the original x from this equation:<\/p>\n\n\n\n 10x – x = 1.6666666\u2026 – 0.1666666\u2026<\/strong><\/p>\n\n\n\n That gives:<\/p>\n\n\n\n 9x = 1.5<\/strong><\/p>\n\n\n\n Now divide both sides by 9:<\/p>\n\n\n\n x = 1.5 \/ 9<\/strong><\/p>\n\n\n\n We can simplify 1.5 as 3\/2:<\/p>\n\n\n\n x = (3\/2) \/ 9 = 3 \/ 18 = 1 \/ 6<\/strong><\/p>\n\n\n\n So, the decimal 0.1666666666\u2026 = 1\/6<\/strong><\/p>\n\n\n\n Repeating decimals occur because of division. When a number doesn\u2019t divide evenly, the remainder repeats. In this case, 1 \u00f7 6 = 0.1666…<\/strong> because 6 doesn’t divide 1 evenly and creates a repeating cycle.<\/p>\n\n\n\n This is one way to define rational numbers<\/strong>: any number that can be expressed as a ratio of two integers. Repeating decimals are always rational, and converting them into fractions involves algebraic manipulation like the example above.<\/p>\n\n\n\n So the decimal 0.1666666666\u2026 is exactly equal to the fraction 1\/6<\/strong>.<\/p>\n\n\n\n 0.16666666666 I need to know what this number is a fraction. The Correct Answer and Explanation is: The decimal number 0.16666666666\u2026 is a repeating decimal, where the digit 6 repeats infinitely. This number can be exactly expressed as the fraction 1\/6. Explanation Decimals that repeat in a consistent pattern can often be written as exact […]<\/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-223946","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223946","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=223946"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223946\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223946"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223946"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223946"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nExplanation<\/h3>\n\n\n\n
\n\n\n\nStep 1: Let x = 0.1666666666…<\/h4>\n\n\n\n
\n\n\n\nWhy Does This Work?<\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-16.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"