{"id":224140,"date":"2025-06-02T18:06:23","date_gmt":"2025-06-02T18:06:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224140"},"modified":"2025-06-02T18:06:25","modified_gmt":"2025-06-02T18:06:25","slug":"what-is-5-6-turned-into-a-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/what-is-5-6-turned-into-a-decimal\/","title":{"rendered":"What is 5\/6 turned into a decimal"},"content":{"rendered":"\n

What is 5\/6 turned into a decimal<\/p>\n\n\n\n

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

Answer:<\/strong>
56=0.833333\u2026\\displaystyle \\frac56 = 0.833333\\ldots (the 3 repeats forever).<\/p>\n\n\n\n

explanation<\/strong><\/p>\n\n\n\n

Converting 5\u204465\u20446 to a decimal asks how many tenths, hundredths, thousandths, and so on equal the same slice of a whole that five sixths represents. Long-division, which repeatedly subtracts multiples of the divisor while keeping track of place value, supplies a dependable route from fraction to decimal.<\/p>\n\n\n\n

Begin by writing 6 (the divisor) outside the bracket and 5 (the dividend) inside. Because 6 exceeds 5, place 0. in the quotient and tack a zero onto the dividend, making 50. Six fits into 50 eight times, because 8\u00d76=488 \u00d7 6 = 48. Record the 8, subtract, and two remains. Drop another zero to produce 20. Six fits into 20 three times (3\u00d76=183 \u00d7 6 = 18), again leaving remainder 2. Each repetition\u2014append zero, divide, subtract\u2014restores that same remainder, so another 3 joins the quotient every cycle. The digits after the initial 8 therefore read 3, 3, 3, continuing forever; the exact decimal is 0.833333\u20260.833333\\ldots.<\/p>\n\n\n\n

Why does the stream of 3\u2019s never end? A rational number yields a terminating decimal only when, after simplification, its denominator is built solely from the primes 2 and 5, because powers of ten are 2n5n2^n5^n. The denominator 6 factors as 2\u00d732 \u00d7 3. The lone factor 3 cannot be balanced by any power of ten, so the remainder can never collapse to zero. Instead, it loops back to 2 after one step, giving a repeating block (called the period) of length 1.<\/p>\n\n\n\n

Mathematicians indicate the endlessly repeating digit by writing 0.83\u203e0.8\\overline{3} (a bar over the 3). Any finite display\u20140.83, 0.833, 0.8333\u2014is merely a rounded snapshot; multiplying that rounded value can introduce small cumulative errors. The issue surfaces in compound-interest forecasts, mortgage amortizations, engineering tolerance charts, and statistical sampling design. Recognizing the repeat alerts you to hidden approximation and error.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

What is 5\/6 turned into a decimal The Correct Answer and Explanation is: Answer:56=0.833333\u2026\\displaystyle \\frac56 = 0.833333\\ldots (the 3 repeats forever). explanation Converting 5\u204465\u20446 to a decimal asks how many tenths, hundredths, thousandths, and so on equal the same slice of a whole that five sixths represents. Long-division, which repeatedly subtracts multiples of the divisor […]<\/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-224140","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224140","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=224140"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224140\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}