{"id":241059,"date":"2025-07-03T14:32:54","date_gmt":"2025-07-03T14:32:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241059"},"modified":"2025-07-03T14:32:56","modified_gmt":"2025-07-03T14:32:56","slug":"which-of-the-following-numbers-are-rational-and-which-are-irrational","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/which-of-the-following-numbers-are-rational-and-which-are-irrational\/","title":{"rendered":"Which of the following numbers are rational, and which are irrational"},"content":{"rendered":"\n

Which of the following numbers are rational, and which are irrational? a. 2.375375 b. 3.0120123 c. \u00e2\u02c6\u0161169 d. 21 e. 3.12 f. \u00e2\u02c6\u0161735 g. 8 h. 0.72 i. 5.626626662<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Here is the classification of the numbers from the image.<\/p>\n\n\n\n

Rational Numbers:<\/strong> a, c, e, g
Irrational Numbers:<\/strong> b, d, f, h<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

To classify these numbers, we must first define rational and irrational numbers. A rational number can be expressed as a ratio or fraction p\/q of two integers, where p is the numerator and q is the non-zero denominator. In decimal form, rational numbers either terminate or have a repeating pattern of digits. An irrational number cannot be expressed as a simple fraction. Its decimal representation is both non-terminating and non-repeating, meaning the digits continue forever without a predictable, repeating block.<\/p>\n\n\n\n

Analysis of the Rational Numbers:<\/strong><\/p>\n\n\n\n

    \n
  • a. 2.375375…<\/strong>\u00a0This number has a clear repeating pattern, where the block of digits “375” repeats indefinitely. Any decimal that has a repeating pattern is a rational number.<\/li>\n\n\n\n
  • c. \u221a169<\/strong>\u00a0The square root of 169 is 13. The number 13 is an integer, which can be expressed as the fraction 13\/1. This fits the definition of a rational number.<\/li>\n\n\n\n
  • e. 3.1\u03052\u0305<\/strong>\u00a0The bar over “12” indicates that these two digits repeat forever, making the number 3.121212… As a repeating decimal, it is a rational number.<\/li>\n\n\n\n
  • g. 35\/x<\/strong>\u00a0This number is shown as a fraction. Assuming the denominator (which is not fully legible) is a non-zero integer, the number is rational by definition, as it is a ratio of two integers.<\/li>\n<\/ul>\n\n\n\n

    Analysis of the Irrational Numbers:<\/strong><\/p>\n\n\n\n

      \n
    • b. 3.0120123…<\/strong>\u00a0This decimal continues forever, but the pattern does not repeat. The sequence seems to be constructed by appending the next integer (012, then 0123). Since the decimal is non-terminating and non-repeating, the number is irrational.<\/li>\n\n\n\n
    • d. 2\u03c0<\/strong>\u00a0The constant pi (\u03c0) is a famous irrational number; its decimal expansion never terminates or repeats. When an irrational number is multiplied by a non-zero rational number like 2, the result remains irrational.<\/li>\n\n\n\n
    • f. \u221a7<\/strong>\u00a0The number 7 is not a perfect square. The square root of any integer that is not a perfect square is an irrational number. Its decimal representation is endless and does not repeat.<\/li>\n\n\n\n
    • h. 5.626626662…<\/strong>\u00a0This number displays a pattern where the quantity of the digit “6” increases between each “2”. This pattern is predictable but not repeating, so the decimal expansion is non-repeating and non-terminating, which makes it an irrational number.<\/li>\n<\/ul>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Which of the following numbers are rational, and which are irrational? a. 2.375375 b. 3.0120123 c. \u00e2\u02c6\u0161169 d. 21 e. 3.12 f. \u00e2\u02c6\u0161735 g. 8 h. 0.72 i. 5.626626662 The Correct Answer and Explanation is: Here is the classification of the numbers from the image. Rational Numbers: a, c, e, gIrrational Numbers: b, d, f, h Explanation […]<\/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-241059","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241059","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=241059"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241059\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}