{"id":167292,"date":"2024-11-15T15:12:26","date_gmt":"2024-11-15T15:12:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167292"},"modified":"2024-11-15T15:12:28","modified_gmt":"2024-11-15T15:12:28","slug":"which-number-is-irrational","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/which-number-is-irrational\/","title":{"rendered":"Which number is irrational"},"content":{"rendered":"\n<p>Which number is irrational? <\/p>\n\n\n\n<p>A. 0.3 <\/p>\n\n\n\n<p>B. [5 <\/p>\n\n\n\n<p>C. 0.777 <\/p>\n\n\n\n<p>D. 00.454445<\/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 correct answer is <strong>D. 0.454445\u2026<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>An irrational number is a number that cannot be expressed as a simple fraction (i.e., a ratio of two integers) and has a non-repeating, non-terminating decimal expansion. Let&#8217;s analyze each option:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A. 0.3<\/strong>: This number is <strong>rational<\/strong>. It can be written as the fraction ( \\frac{3}{10} ), where both the numerator (3) and the denominator (10) are integers. The decimal expansion is terminating, and thus it is a rational number.<\/li>\n\n\n\n<li><strong>B. [5<\/strong>: It seems like there is a formatting error in the option (it should be a number or a decimal), but from the context, if this refers to a valid rational number such as ( \\frac{5}{1} ), it would be a <strong>rational number<\/strong>. It can be expressed as a ratio of two integers.<\/li>\n\n\n\n<li><strong>C. 0.777\u2026<\/strong>: This number is <strong>rational<\/strong>. The decimal repeats (the digit &#8220;7&#8221; repeats infinitely), and any number with a repeating decimal can be written as a fraction. Specifically, ( 0.777\u2026 ) is equal to ( \\frac{7}{9} ), which is a ratio of two integers, so it is rational.<\/li>\n\n\n\n<li><strong>D. 0.454445\u2026<\/strong>: This number is <strong>irrational<\/strong>. The decimal expansion goes on infinitely without repeating a specific pattern, making it impossible to express it as a fraction. The non-repeating, non-terminating nature of the decimal expansion indicates that the number cannot be written as a ratio of two integers. This is a key characteristic of irrational numbers.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rational numbers<\/strong> can be written as fractions and either have a terminating or repeating decimal expansion.<\/li>\n\n\n\n<li><strong>Irrational numbers<\/strong> cannot be written as fractions and have a non-terminating, non-repeating decimal expansion.<br>Thus, option D, <strong>0.454445\u2026<\/strong>, is the irrational number.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Which number is irrational? A. 0.3 B. [5 C. 0.777 D. 00.454445 The Correct Answer and Explanation is: The correct answer is D. 0.454445\u2026. Explanation: An irrational number is a number that cannot be expressed as a simple fraction (i.e., a ratio of two integers) and has a non-repeating, non-terminating decimal expansion. Let&#8217;s analyze each [&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-167292","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167292","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=167292"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167292\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}