{"id":22755,"date":"2025-06-16T21:48:42","date_gmt":"2025-06-16T21:48:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=22755"},"modified":"2025-06-16T21:48:47","modified_gmt":"2025-06-16T21:48:47","slug":"which-number-is-rational","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-number-is-rational\/","title":{"rendered":"Which number is rational"},"content":{"rendered":"\n

Which number is rational? <\/p>\n\n\n\n

1. -2.1010010001\u2026 <\/p>\n\n\n\n

2. -0.8974512\u2026 <\/p>\n\n\n\n

3. 1.2547569\u2026 <\/p>\n\n\n\n

4. 5.3333333\u2026<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

The number that is rational among the options is:<\/p>\n\n\n\n

4. 5.3333333…<\/strong><\/p>\n\n\n\n

\n\n\n\n

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

A rational number<\/strong> is any number that can be expressed as a fraction pq\\frac{p}{q}, where pp and qq are integers and q\u22600q \\neq 0. Rational numbers have decimal expansions that either terminate<\/strong> (end after a finite number of digits) or repeat a pattern indefinitely<\/strong> (repeating decimals).<\/p>\n\n\n\n

Let’s analyze each number:<\/p>\n\n\n\n

    \n
  1. -2.1010010001…<\/strong> This decimal appears to have a non-repeating, irregular pattern: the digits after the decimal are 1,0,1,0,0,1,0,0,0,1… with no obvious repeating cycle. Such a number is likely irrational<\/strong>, meaning it cannot be expressed as a simple fraction. Irrational numbers have non-terminating, non-repeating decimals.<\/li>\n\n\n\n
  2. -0.8974512…<\/strong> This number shows a decimal expansion with digits that do not repeat or terminate visibly. Without a repeating pattern, it is likely an irrational number.<\/li>\n\n\n\n
  3. 1.2547569…<\/strong> Similar to option 2, this number has a decimal part that does not terminate or show a repeating pattern. Hence, it is likely irrational.<\/li>\n\n\n\n
  4. 5.3333333…<\/strong> This decimal expansion is a clear repeating decimal: the digit 3 repeats indefinitely. This repeating decimal can be written exactly as the fraction 163\\frac{16}{3} (since 5.3333…=5+13=153+13=1635.3333… = 5 + \\frac{1}{3} = \\frac{15}{3} + \\frac{1}{3} = \\frac{16}{3}).<\/li>\n<\/ol>\n\n\n\n

    Because this number can be expressed as a fraction of two integers, it is rational<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Summary<\/h3>\n\n\n\n
      \n
    • Rational numbers = decimals that terminate or have a repeating pattern.<\/li>\n\n\n\n
    • Irrational numbers = decimals that neither terminate nor repeat.<\/li>\n\n\n\n
    • Option 4 has a repeating decimal and is therefore rational.<\/li>\n\n\n\n
    • Options 1, 2, and 3 appear non-repeating and non-terminating, so are irrational.<\/li>\n<\/ul>\n\n\n\n

      Final answer: 4. 5.3333333… is rational.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

      Which number is rational? 1. -2.1010010001\u2026 2. -0.8974512\u2026 3. 1.2547569\u2026 4. 5.3333333\u2026 The correct answer and explanation is: The number that is rational among the options is: 4. 5.3333333… Explanation: A rational number is any number that can be expressed as a fraction pq\\frac{p}{q}, where pp and qq are integers and q\u22600q \\neq 0. Rational […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-22755","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22755","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=22755"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22755\/revisions"}],"predecessor-version":[{"id":22756,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22755\/revisions\/22756"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22755"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22755"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}