{"id":40496,"date":"2025-06-27T18:16:22","date_gmt":"2025-06-27T18:16:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=40496"},"modified":"2025-06-27T18:16:23","modified_gmt":"2025-06-27T18:16:23","slug":"a-rational-number-is-either-terminating-or-non-terminating-repeating","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-rational-number-is-either-terminating-or-non-terminating-repeating\/","title":{"rendered":"A rational number is either terminating or non terminating repeating."},"content":{"rendered":"\n<p>U uestions Con ith 7] repeating. Sol. A rational number is either terminating or non terminating repeating. An irrational number is non-terminating and non- [CBSE Marking Scheme, 2016] 3 U Q. 4. Calculate\\frac{3}{8} in the decimal form. 8 3 Sol. \\frac{3}{8} = \\frac{3}{2^3} 3\\times5^3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-418.png\" alt=\"\" class=\"wp-image-40507\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-418.png 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-418-300x169.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-418-768x432.png 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the decimal form of the fraction 38\\frac{3}{8}, we proceed as follows:<\/p>\n\n\n\n<p>38=323\\frac{3}{8} = \\frac{3}{2^3}<\/p>\n\n\n\n<p>Since the denominator is composed only of the prime factor 2, this indicates that the fraction is <strong>a terminating decimal<\/strong>. Let&#8217;s perform the division:<\/p>\n\n\n\n<p>38=0.375\\frac{3}{8} = 0.375<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>A <strong>rational number<\/strong> is defined as a number that can be expressed as the ratio of two integers where the denominator is not zero. Rational numbers include both <strong>terminating<\/strong> and <strong>repeating decimals<\/strong>. A decimal terminates if, when the fraction is fully simplified, its denominator has no prime factors other than 2 or 5. If any other prime factor remains in the denominator, the decimal form will be repeating and non-terminating.<\/p>\n\n\n\n<p>In the case of 38\\frac{3}{8}, the denominator is 8, which equals 232^3. It contains only the prime factor 2, making it a rational number with a terminating decimal.<\/p>\n\n\n\n<p>To understand this deeper, consider converting fractions to decimal form by dividing the numerator by the denominator. When we divide 3 by 8, we get:<\/p>\n\n\n\n<p>3\u00f78=0.3753 \\div 8 = 0.375<\/p>\n\n\n\n<p>This means that 38=0.375\\frac{3}{8} = 0.375 exactly. There is no repeating part, and the decimal ends after three digits.<\/p>\n\n\n\n<p>In contrast, irrational numbers cannot be written as fractions of integers. They have decimal expansions that are both non-terminating and non-repeating. Examples include \u03c0\\pi and 2\\sqrt{2}. These numbers defy exact expression in decimal or fractional form.<\/p>\n\n\n\n<p>To summarize, 38\\frac{3}{8} is a rational number with a terminating decimal, and its exact decimal representation is:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1269.jpeg\" alt=\"\" class=\"wp-image-40514\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1269.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1269-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1269-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>U uestions Con ith 7] repeating. Sol. A rational number is either terminating or non terminating repeating. An irrational number is non-terminating and non- [CBSE Marking Scheme, 2016] 3 U Q. 4. Calculate\\frac{3}{8} in the decimal form. 8 3 Sol. \\frac{3}{8} = \\frac{3}{2^3} 3\\times5^3 The Correct Answer and Explanation is: To calculate the decimal form [&hellip;]<\/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-40496","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40496","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=40496"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40496\/revisions"}],"predecessor-version":[{"id":40516,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40496\/revisions\/40516"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}