{"id":167260,"date":"2024-11-15T14:36:23","date_gmt":"2024-11-15T14:36:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167260"},"modified":"2024-11-15T14:36:25","modified_gmt":"2024-11-15T14:36:25","slug":"why-is-70-300722-a-rational-number","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/why-is-70-300722-a-rational-number\/","title":{"rendered":"Why is 70.300722 a rational number"},"content":{"rendered":"\n<p>Share<\/p>\n\n\n\n<p>You said:<br>Why is 70.300722 a rational number<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The number 70.300722 is a <strong>rational number<\/strong> because it can be expressed as a ratio of two integers, which is the defining characteristic of rational numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Understanding Rational Numbers:<\/h3>\n\n\n\n<p>A <strong>rational number<\/strong> is any number that can be written in the form of a fraction or ratio, where both the numerator and the denominator are integers, and the denominator is not zero. In other words, a rational number can be represented as ( \\frac{p}{q} ), where ( p ) and ( q ) are integers and ( q \\neq 0 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Decimal Representation:<\/h3>\n\n\n\n<p>The given number, <strong>70.300722<\/strong>, is a <strong>terminating decimal<\/strong> because it has a finite number of digits after the decimal point. Rational numbers can either have:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Terminating decimals<\/strong>: These decimals end after a finite number of digits (like 0.75 or 2.5).<\/li>\n\n\n\n<li><strong>Repeating decimals<\/strong>: These decimals have a repeating block of digits that go on infinitely (like 0.333\u2026 or 1.666\u2026).<\/li>\n<\/ol>\n\n\n\n<p>In the case of <strong>70.300722<\/strong>, the decimal part is <strong>300722<\/strong>, which ends after six digits. Since it terminates, we know that it is a rational number. Any terminating decimal can be converted into a fraction, which proves its rationality.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Converting 70.300722 into a Fraction:<\/h3>\n\n\n\n<p>To express <strong>70.300722<\/strong> as a fraction:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Consider the number as <strong>70300722\/1000000<\/strong> by moving the decimal point six places to the right.<\/li>\n\n\n\n<li>Simplify the fraction if possible. The number 70300722 and 1000000 can be divided by their greatest common divisor (GCD), which is 2:<br>[<br>\\frac{70300722}{1000000} = \\frac{35150361}{500000}<br>]<br>Thus, <strong>70.300722<\/strong> is equivalent to the fraction ( \\frac{35150361}{500000} ), which is the ratio of two integers.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>Since <strong>70.300722<\/strong> can be expressed as the ratio of two integers, it is a rational number. Rational numbers include both integers and fractions, and their decimal representations can either terminate or repeat. Therefore, <strong>70.300722<\/strong> qualifies as a rational number because it has a finite decimal expansion and can be expressed as a fraction.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Share You said:Why is 70.300722 a rational number The Correct Answer and Explanation is: The number 70.300722 is a rational number because it can be expressed as a ratio of two integers, which is the defining characteristic of rational numbers. Understanding Rational Numbers: A rational number is any number that can be written in the [&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-167260","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167260","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=167260"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167260\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}