{"id":24935,"date":"2022-06-05T15:00:44","date_gmt":"2022-06-05T09:30:44","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=24935"},"modified":"2022-05-23T15:57:32","modified_gmt":"2022-05-23T10:27:32","slug":"ncert-solutions-for-class-10-maths-chapter-1-ex-1-4","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-4\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4"},"content":{"rendered":"

These NCERT Solutions for Class 10 Maths<\/a> Chapter 1 Real Numbers Ex 1.4 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers<\/h2>\n

Exercise 1.4<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nWithout actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansion:
\n(i) \\(\\frac { 13 }{ 3125 }\\)
\n(ii) \\(\\frac { 17 }{ 8 }\\)
\n(iii) \\(\\frac { 64 }{ 455 }\\)
\n(iv) \\(\\frac{15}{1600}\\)
\n(v) \\(\\frac { 29 }{ 343 }\\)
\n(vi) \\(\\frac{23}{2^{3} 5^{2}}\\)
\n(vii) \\(\\frac{129}{2^{2} 5^{7} 7^{5}}\\)
\n(viii) \\(\\frac { 6 }{ 15 }\\)
\n(ix) \\(\\frac { 35 }{ 50 }\\)
\n(x) \\(\\frac { 77 }{ 210 }\\)
\nSolution:
\n(i) \\(\\frac { 13 }{ 3125 }\\) = \\(\\frac{17}{2 \\times 2 \\times 2}\\) = \\(\\frac{17}{2^{3}}\\)
\nBecause the denominator can be in the form 2n<\/sup> 5n<\/sup>, hence it will have terminating decimal expansion.<\/p>\n

(ii) \\(\\frac { 17 }{ 8 }\\) = \\(\\frac { 17 }{ 8 }\\)
\nIt will have terminating decimal expansion.<\/p>\n

(iii) \\(\\frac { 64 }{ 455 }\\) = \\(\\frac{64}{5 \\times 7 \\times 13}\\)
\nNon terminating repeating decimal expansion.<\/p>\n

(iv) \\(\\frac{15}{1600}\\) = \\(\\frac{15}{2^{2} \\times 5^{2}}\\)
\nIt will have terminating decimal expansion.<\/p>\n

(v) \\(\\frac { 29 }{ 343 }\\) = \\(\\frac{29}{7^{3}}\\)
\nNon terminating repeating decimal expansion.<\/p>\n

(vi) \\(\\frac{23}{2^{3} 5^{2}}\\)
\nIt will have terminating decimal expansion.<\/p>\n

(vii) \\(\\frac{129}{2^{2} 5^{7} 7^{5}}\\)
\nNon terminating repeating decimal expansion.<\/p>\n

(viii) \\(\\frac { 6 }{ 15 }\\) = \\(\\frac{6}{3 \\times 5}\\)
\nIt will have terminating decimal expansion.<\/p>\n

(ix) \\(\\frac { 35 }{ 50 }\\) = \\(\\frac{35}{2 \\times 5^{2}}\\)
\nIt will have terminating decimal expansion.<\/p>\n

(x) \\(\\frac { 77 }{ 210 }\\) = \\(\\frac{17}{2 \\times 3 \\times 5 \\times 7}\\)
\nNon terminating repeating decimal expansion.<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nWrite down the decimal expansion of those rational numbers in Question 1 above which terminating decimal expansions.
\nSolution:
\n(i) \\(\\frac { 13 }{ 3125 }\\) = 0.00146
\n(ii) \\(\\frac { 17 }{ 8 }\\) = 2.125
\n(iii) \\(\\frac { 15 }{ 1600 }\\) = 0.009375
\n(iv) \\(\\frac{23}{2^{3} 5^{2}}\\) = \\(\\frac { 23 }{ 200 }\\) = 0.115
\n(v) \\(\\frac { 6 }{ 15 }\\) = 0.4
\n(vi) \\(\\frac { 35 }{ 50 }\\) = 0.7<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nThe following real numbers have decimal expansions as given below. In each case decide whether they are rational or not. If they are rational and of the form \\(\\frac { p }{ q }\\), what can you say about the prime factors of q?
\n(i) 43.123456789
\n(ii) 0.120120012000120000
\n(iii) \\(43 . \\overline{123456789}\\)
\nSolution:
\n(i) 43.123456789
\n\\(=\\frac{43123456789}{1000000000}=\\frac{43123456789}{2^{9} 5^{9}}\\)
\nit is a rational, number The prime factors of q are 29<\/sup>59<\/sup><\/p>\n

(ii) 0.120120012000120000 …….
\n\\(\\begin{aligned}
\n&=\\frac{120120012000012}{100000000000000 \\ldots \\ldots . .} \\\\
\n&=\\frac{120120012000012}{\\left(2^{1} \\times 2^{2} \\times 2^{3} \\ldots . .\\right) \\times\\left(5^{1} \\times 5^{2} \\times 5^{3} . \\ldots .\\right)}
\n\\end{aligned}\\)
\nit is a rational number The prime factors of q are (21<\/sup> x 2\u00b2 x 2\u00b3 ….) x (51<\/sup> x 5\u00b2 x 5\u00b3 ….)<\/p>\n

(iii) \\(43 . \\overline{123456789}\\)
\nIt is not-terminating decimal expansion.
\nBut it is a rational number, whose prime factors of q will also have a factor other than 2 or 5.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.4 Question 1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal …<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[2],"tags":[],"yoast_head":"\nNCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 Questions and Answers are prepared by our highly skilled subject experts. 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