{"id":166658,"date":"2024-11-13T23:42:11","date_gmt":"2024-11-13T23:42:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=166658"},"modified":"2024-11-13T23:42:13","modified_gmt":"2024-11-13T23:42:13","slug":"which-number-produces-a-rational-number-when-added-to-0-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/13\/which-number-produces-a-rational-number-when-added-to-0-5\/","title":{"rendered":"Which number produces a rational number when added to 0.5"},"content":{"rendered":"\n

Which number produces a rational number when added to 0.5?
A. \u20131.73205081\u2026
B. 1\/4
C. 0.54732871\u2026
D. \u221a3<\/p>\n\n\n\n

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

The correct answer is B. 1\/4<\/strong>.<\/p>\n\n\n\n

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

To determine which number produces a rational number when added to 0.5, we need to review the definitions of rational and irrational numbers.<\/p>\n\n\n\n

    \n
  • Rational numbers<\/strong> are numbers that can be expressed as the quotient of two integers (i.e., as fractions) in the form ( \\frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \\neq 0 ). Examples of rational numbers include ( 1\/4, -2, 0.5, ) and ( 7 ). Rational numbers have either terminating or repeating decimal expansions.<\/li>\n\n\n\n
  • Irrational numbers<\/strong> are numbers that cannot be written as the quotient of two integers. They cannot be expressed as a fraction, and their decimal expansions neither terminate nor repeat. Examples include ( \\pi ), ( \\sqrt{2} ), and ( \\sqrt{3} ).<\/li>\n<\/ul>\n\n\n\n

    Now, let’s evaluate each option and see which one, when added to 0.5, results in a rational number.<\/p>\n\n\n\n

      \n
    1. Option A: -1.73205081\u2026<\/strong>
      This number is the decimal approximation of ( -\\sqrt{3} ), which is an irrational number<\/strong>. Adding an irrational number to a rational number (0.5) results in an irrational number. Therefore, the sum is irrational.<\/li>\n\n\n\n
    2. Option B: 1\/4<\/strong>
      This is a rational number<\/strong> because it can be written as the fraction ( \\frac{1}{4} ). When we add a rational number (1\/4) to another rational number (0.5), the result is still a rational number. Specifically, ( 0.5 + 1\/4 = 0.5 + 0.25 = 0.75 ), which is rational.<\/li>\n\n\n\n
    3. Option C: 0.54732871\u2026<\/strong>
      This is a non-repeating, non-terminating decimal<\/strong>, which indicates that the number is irrational<\/strong>. When you add an irrational number to a rational number, the result is irrational. Therefore, the sum is irrational.<\/li>\n\n\n\n
    4. Option D: ( \\sqrt{3} )<\/strong>
      The square root of 3 is an irrational number<\/strong>, as its decimal expansion does not terminate or repeat. Adding an irrational number to a rational number results in an irrational sum, so the result is irrational.<\/li>\n<\/ol>\n\n\n\n

      Thus, the only option that produces a rational sum when added to 0.5 is B. 1\/4<\/strong>, since the sum is 0.75, which is a rational number.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Which number produces a rational number when added to 0.5?A. \u20131.73205081\u2026B. 1\/4C. 0.54732871\u2026D. \u221a3 The Correct Answer and Explanation is: The correct answer is B. 1\/4. Explanation: To determine which number produces a rational number when added to 0.5, we need to review the definitions of rational and irrational numbers. Now, let’s evaluate each option […]<\/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-166658","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166658","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=166658"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166658\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}