{"id":229212,"date":"2025-06-08T04:15:55","date_gmt":"2025-06-08T04:15:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229212"},"modified":"2025-06-08T04:15:57","modified_gmt":"2025-06-08T04:15:57","slug":"from-the-middle-into-the-correct-red-box-according-to-whether-the-value-is-rational-or-irrational-rational-a","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/from-the-middle-into-the-correct-red-box-according-to-whether-the-value-is-rational-or-irrational-rational-a\/","title":{"rendered":"FROM THE MIDDLE INTO THE CORRECT RED BOX ACCORDING TO WHETHER THE VALUE IS RATIONAL OR IRRATIONAL RATIONAL A"},"content":{"rendered":"\n

FROM THE MIDDLE INTO THE CORRECT RED BOX ACCORDING TO WHETHER THE VALUE IS RATIONAL OR IRRATIONAL RATIONAL A<\/p>\n\n\n\n

B -33 C
D 0.7 E 13.654\u2026 F
G<\/p>\n\n\n\n

H<\/p>\n\n\n\n

I
J 8.462\u2026 IRRATIONAL
rrational Numbers Activity – 6912304 DRAG AND DROP EACH PIECE FROM THE MIDDLE INTO THE CORRECT RED BOX ACCORDING TO WHETHER THE VALUE IS RATIONAL OR IRRATIONAL RATIONAL A<\/p>\n\n\n\n

B -33 C
D 0.7 E 13.654\u2026 F
G<\/p>\n\n\n\n

H<\/p>\n\n\n\n

I
J 8.462\u2026 IRRATIONAL<\/p>\n\n\n\n

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

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

\u2705 Correct Answers:<\/h3>\n\n\n\n

RATIONAL Numbers<\/strong> (can be expressed as a fraction or have a terminating\/repeating decimal):<\/p>\n\n\n\n

    \n
  • A. 12\u00be<\/strong> \u2192 Rational (Mixed number = 51\/4)<\/li>\n\n\n\n
  • B. -33<\/strong> \u2192 Rational (Integer = -33\/1)<\/li>\n\n\n\n
  • D. 0.7<\/strong> \u2192 Rational (Terminating decimal = 7\/10)<\/li>\n\n\n\n
  • E. 13.654<\/strong> \u2192 Rational (Terminating decimal = 13654\/1000)<\/li>\n\n\n\n
  • G. 4\u221a100<\/strong> \u2192 Rational (\u221a100 = 10 \u2192 4 \u00d7 10 = 40)<\/li>\n\n\n\n
  • H. -\u2153<\/strong> \u2192 Rational (Fraction = -1\/3)<\/li>\n\n\n\n
  • J. 8.462<\/strong> \u2192 Rational (Terminating decimal = 8462\/1000)<\/li>\n<\/ul>\n\n\n\n

    IRRATIONAL Numbers<\/strong> (non-repeating, non-terminating decimals or roots of non-perfect squares):<\/p>\n\n\n\n

      \n
    • C. \u221a22<\/strong> \u2192 Irrational (\u221a22 \u2248 4.690\u2026 does not repeat or terminate)<\/li>\n\n\n\n
    • F. 3\u03c0<\/strong> \u2192 Irrational (\u03c0 is irrational \u2192 3\u03c0 is irrational)<\/li>\n\n\n\n
    • I. \u221a200<\/strong> \u2192 Irrational (\u221a200 \u2248 14.142\u2026 not a perfect square)<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      \ud83e\udde0 Explanation (300 Words):<\/h3>\n\n\n\n

      The classification of numbers into rational<\/strong> and irrational<\/strong> is fundamental in mathematics.<\/p>\n\n\n\n

      A rational number<\/strong> is any number that can be written as a fraction of two integers<\/strong>, where the denominator is not zero. This includes:<\/p>\n\n\n\n

        \n
      • Whole numbers<\/strong> (e.g., -33),<\/li>\n\n\n\n
      • Fractions<\/strong> (like -\u2153 or 12\u00be),<\/li>\n\n\n\n
      • Terminating decimals<\/strong> (e.g., 0.7 or 8.462),<\/li>\n\n\n\n
      • And repeating decimals<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        In this activity:<\/p>\n\n\n\n

          \n
        • 12\u00be<\/strong> is a mixed number which is equivalent to 51\/4, so it is rational.<\/li>\n\n\n\n
        • -33<\/strong>, an integer, is rational.<\/li>\n\n\n\n
        • 0.7<\/strong>, 13.654<\/strong>, and 8.462<\/strong> are all terminating decimals, which can be expressed as fractions.<\/li>\n\n\n\n
        • -\u2153<\/strong> is already a fraction.<\/li>\n\n\n\n
        • 4\u221a100<\/strong> simplifies to 4 \u00d7 10 = 40, which is also rational.<\/li>\n<\/ul>\n\n\n\n

          On the other hand, an irrational number<\/strong> cannot be written as a fraction. These numbers have non-terminating and non-repeating decimals<\/strong>. Common examples include:<\/p>\n\n\n\n

            \n
          • Square roots of non-perfect squares (like \u221a22 or \u221a200)<\/li>\n\n\n\n
          • Irrational constants like \u03c0<\/strong><\/li>\n<\/ul>\n\n\n\n

            In this exercise:<\/p>\n\n\n\n

              \n
            • \u221a22<\/strong> and \u221a200<\/strong> are irrational because 22 and 200 are not perfect squares, so their square roots are infinite non-repeating decimals.<\/li>\n\n\n\n
            • 3\u03c0<\/strong> is irrational because \u03c0 itself is irrational, and multiplying it by a rational number does not make it rational.<\/li>\n<\/ul>\n\n\n\n

              Recognizing whether a number is rational or irrational helps in algebra, calculus, and real-world measurements. It also reinforces understanding of number properties and how they behave within mathematical operations.<\/p>\n\n\n\n

              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

              FROM THE MIDDLE INTO THE CORRECT RED BOX ACCORDING TO WHETHER THE VALUE IS RATIONAL OR IRRATIONAL RATIONAL A B -33 CD 0.7 E 13.654\u2026 FG H IJ 8.462\u2026 IRRATIONALrrational Numbers Activity – 6912304 DRAG AND DROP EACH PIECE FROM THE MIDDLE INTO THE CORRECT RED BOX ACCORDING TO WHETHER THE VALUE IS RATIONAL OR […]<\/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-229212","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229212","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=229212"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229212\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}