{"id":10431,"date":"2022-04-09T20:57:11","date_gmt":"2022-04-09T15:27:11","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10431"},"modified":"2022-04-09T22:32:34","modified_gmt":"2022-04-09T17:02:34","slug":"without-actually-performing-the-long-division-state-whether-the-following-rational-numbers-will-have-a-terminating-decimal-expansion-or-a-non-terminating-repeating-decimal-expansion","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/without-actually-performing-the-long-division-state-whether-the-following-rational-numbers-will-have-a-terminating-decimal-expansion-or-a-non-terminating-repeating-decimal-expansion\/","title":{"rendered":"Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion :"},"content":{"rendered":"<p><strong>Question<\/strong> : Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion :<\/p>\n<p>(i) \\(13\\over 3125\\)<\/p>\n<p>(ii)&nbsp; \\(17\\over 8\\)<\/p>\n<p>(iii)&nbsp; \\(64\\over 455\\)<\/p>\n<p>(iv)&nbsp; \\(15\\over 1600\\)<\/p>\n<p>(v)&nbsp; \\(29\\over 343\\)<\/p>\n<p>(vi)&nbsp; \\(23\\over {2^3 5^2}\\)<\/p>\n<p>(vii)&nbsp; \\(129\\over {2^2 5^7 7^5}\\)<\/p>\n<p>(viii)&nbsp; \\(6\\over 15\\)<\/p>\n<p>(ix)&nbsp; \\(35\\over 50\\)<\/p>\n<p>(x)&nbsp; \\(77\\over 210\\)<\/p>\n<p><strong>Solution<\/strong> :<\/p>\n<p><strong>(i)<\/strong>&nbsp; Since the factors of the denominator 3125 are \\(2^0 \\times 5^5\\). Therefore \\(13\\over 3125\\) is <strong>a terminating decimal<\/strong>.<\/p>\n<p><strong>(ii)<\/strong>&nbsp; Since the factors of the denominator 8 are \\(2^3 \\times 5^0\\). So, \\(17\\over 8\\) is <strong>a terminating decimal<\/strong>.<\/p>\n<p><strong>(iii)<\/strong>&nbsp; Since the factors of the denominator 455 is not in the form \\(2^n \\times 5^m\\). Therefore \\(64\\over 55\\) is <strong>a non-terminating repeating decimal<\/strong>.<\/p>\n<p><strong>(iv)<\/strong>&nbsp; Since the factors of the denominator 1600 are \\(2^6 \\times 5^2\\). Therefore \\(15\\over 1600\\) is <strong>a terminating decimal<\/strong>.<\/p>\n<p><strong>(v)<\/strong>&nbsp; Since the factors of the denominator 343 is not of the form \\(2^n \\times 5^m\\). Therefore it is <strong>a non-terminating repeating decimal<\/strong>.<\/p>\n<p><strong>(vi)<\/strong>&nbsp; Since the factors of the denominator is of form \\(2^3 \\times 5^2\\). Therefore it is <strong>a terminating decimal<\/strong>.<\/p>\n<p><strong>(vii)<\/strong>&nbsp; Since the factors of the denominator \\(2^2 \\times 5^7 \\times 7^5\\) is not of the form \\(2^n \\times 5^m\\). Therefore it is <strong>a non-terminating repeating decimal<\/strong>.<\/p>\n<p><strong>(viii)<\/strong>&nbsp; \\(16\\over 5\\) = \\(2\\over 5\\) here the factors of the denominator 5 are \\(2^0 \\times 5^1\\). Therefore it is <strong>a terminating decimal<\/strong>.<\/p>\n<p><strong>(ix)<\/strong>&nbsp; Since the factors of the denominator 50 are \\(2^1 \\times 5^2\\). Therefore \\(35\\over 30\\) is <strong>a terminating decimal<\/strong>.<\/p>\n<p><strong>(x)<\/strong>&nbsp; Since the factors of the denominator 210 is not of the form \\(2^n \\times 5^m\\). Therefore \\(77\\over 210\\) is <strong>a non-terminating rrepeating decimal<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Question : Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion : (i) \\(13\\over 3125\\) (ii)&nbsp; \\(17\\over 8\\) (iii)&nbsp; \\(64\\over 455\\) (iv)&nbsp; \\(15\\over 1600\\) (v)&nbsp; \\(29\\over 343\\) (vi)&nbsp; \\(23\\over {2^3 5^2}\\) (vii)&nbsp; \\(129\\over {2^2 5^7 7^5}\\) (viii)&nbsp; \\(6\\over 15\\) (ix)&nbsp; &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/without-actually-performing-the-long-division-state-whether-the-following-rational-numbers-will-have-a-terminating-decimal-expansion-or-a-non-terminating-repeating-decimal-expansion\/\"> <span class=\"screen-reader-text\">Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion :<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,909],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - 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