{"id":156156,"date":"2024-10-17T04:46:00","date_gmt":"2024-10-17T04:46:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156156"},"modified":"2024-10-17T04:46:03","modified_gmt":"2024-10-17T04:46:03","slug":"written-as-fractions-the-decimal-numbers-and-are-and-respectively","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/written-as-fractions-the-decimal-numbers-and-are-and-respectively\/","title":{"rendered":"written as fractions, the decimal numbers and are and , respectively"},"content":{"rendered":"\n<p>written as fractions, the decimal numbers and are and , respectively. can you see a pattern? use this knowledge to convert 0.0625 into a fraction. then find its simplest form.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To convert the decimal number 0.0625 into a fraction and find its simplest form, let\u2019s first observe some decimal to fraction conversions to identify a pattern.<\/p>\n\n\n\n<p>Common decimal equivalents include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0.1 = 1\/10<\/li>\n\n\n\n<li>0.25 = 1\/4<\/li>\n\n\n\n<li>0.5 = 1\/2<\/li>\n\n\n\n<li>0.75 = 3\/4<\/li>\n\n\n\n<li>0.125 = 1\/8<\/li>\n\n\n\n<li>0.0625 = ?<\/li>\n<\/ul>\n\n\n\n<p>From this, we see that many decimal numbers can be expressed as fractions, often with powers of 2 or 5 as denominators. Specifically, fractions that have a denominator of 10, 100, or 1000 are common in decimal representation.<\/p>\n\n\n\n<p>Now, let\u2019s convert 0.0625 into a fraction. The decimal 0.0625 can be read as \u201c62.5 thousandths,\u201d which translates to:<\/p>\n\n\n\n<p>[<br>0.0625 = \\frac{625}{10000}<br>]<\/p>\n\n\n\n<p>Next, we can simplify this fraction. To do this, we need to find the greatest common divisor (GCD) of the numerator (625) and the denominator (10,000).<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding the GCD<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factorization of 625 is (5^4) (since (625 = 5 \\times 5 \\times 5 \\times 5)).<\/li>\n\n\n\n<li>The prime factorization of 10,000 is (10^4 = (2 \\times 5)^4 = 2^4 \\times 5^4).<\/li>\n<\/ul>\n\n\n\n<p>From the prime factorizations, we see that the GCD is (5^4 = 625).<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Dividing both the numerator and denominator by their GCD<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>[<br>\\frac{625 \\div 625}{10000 \\div 625} = \\frac{1}{16}<br>]<\/p>\n\n\n\n<p>Thus, (0.0625) simplifies to (\\frac{1}{16}).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>In summary, the decimal (0.0625) can be converted into the fraction (\\frac{625}{10000}). By finding the GCD of 625 and 10,000, we simplify it to (\\frac{1}{16}), the simplest form of this fraction. This process illustrates the relationship between decimals and fractions and the importance of simplification in expressing numbers in their most concise form.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>written as fractions, the decimal numbers and are and , respectively. can you see a pattern? use this knowledge to convert 0.0625 into a fraction. then find its simplest form. The Correct Answer and Explanation is : To convert the decimal number 0.0625 into a fraction and find its simplest form, let\u2019s first observe some [&hellip;]<\/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-156156","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156156","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=156156"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156156\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}