{"id":249190,"date":"2025-07-09T04:25:04","date_gmt":"2025-07-09T04:25:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249190"},"modified":"2025-07-09T04:25:06","modified_gmt":"2025-07-09T04:25:06","slug":"find-the-decimal-representation-of-the-following-rational-numbers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/find-the-decimal-representation-of-the-following-rational-numbers\/","title":{"rendered":"\u00a0Find the decimal representation of the following rational numbers."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Of course, here are the decimal representations for the given rational numbers, along with a detailed explanation.<\/p>\n\n\n\n

Correct Answer:<\/strong><\/p>\n\n\n\n

(i) -12\/13 = -0.923076
(ii) -1525\/50 = -30.5
(iii) -127\/7 = -18.142857
(iv) -539\/80 = -6.7375<\/p>\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

To find the decimal representation of a rational number, which is a number expressed as a fraction, we perform the division of the numerator by the denominator. The resulting decimal will either be terminating (it ends) or non-terminating repeating (it has a sequence of digits that repeats forever). A fraction results in a terminating decimal if the prime factors of its denominator, once the fraction is in its simplest form, are only 2s and 5s.<\/p>\n\n\n\n

(i) For the fraction -12\/13, the denominator is 13. Since 13 is a prime number other than 2 or 5, the decimal will be repeating. Performing the long division of 12 by 13, we find a repeating pattern. The division yields 0.923076923076…, where the block of digits “923076” repeats indefinitely. We use a bar over the repeating block to represent this. Therefore, the decimal representation is -0.923076.<\/p>\n\n\n\n

(ii) For the fraction -1525\/50, we first examine the denominator, 50. Its prime factorization is 2 \u00d7 5\u00b2, which contains only the primes 2 and 5. This indicates the decimal will terminate. We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, 25, which gives -61\/2. Dividing -61 by 2 is straightforward and results in -30.5. The division ends, confirming it is a terminating decimal.<\/p>\n\n\n\n

(iii) The fraction -127\/7 has a denominator of 7, which is a prime number that is not 2 or 5. Consequently, we expect a non-terminating, repeating decimal. By dividing 127 by 7, we get 18 with a remainder. Continuing the division on the remainder gives a repeating sequence of digits. The result is 18.142857142857…, with the block “142857” repeating. So, the decimal representation is -18.142857.<\/p>\n\n\n\n

(iv) Lastly, for the fraction -539\/80, the denominator is 80. The prime factorization of 80 is 2\u2074 \u00d7 5. Since the only prime factors are 2 and 5, the decimal representation will be terminating. Dividing -539 by 80 using long division gives the exact value of -6.7375. The division process concludes with a remainder of zero, producing a finite number of decimal digits.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: Of course, here are the decimal representations for the given rational numbers, along with a detailed explanation. Correct Answer: (i) -12\/13 = -0.923076(ii) -1525\/50 = -30.5(iii) -127\/7 = -18.142857(iv) -539\/80 = -6.7375 Explanation: To find the decimal representation of a rational number, which is a number expressed as a […]<\/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-249190","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249190","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=249190"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249190\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}