{"id":6005,"date":"2023-07-14T04:45:42","date_gmt":"2023-07-14T04:45:42","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6005"},"modified":"2023-07-23T05:42:10","modified_gmt":"2023-07-23T05:42:10","slug":"ncert-solutions-class-10-maths-chapter-1-real-numbers-ex-1-4","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-1-real-numbers-ex-1-4\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 1 Real Numbers Ex 1.4"},"content":{"rendered":"<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><br \/>\n<strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 1 (Real Numbers)\u00a0<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 1 Real Numbers\u00a0 <\/strong>Exercise 1.4 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #ff0000;\"><strong>Chapter : 1 Real Numbers<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-1-real-numbers-ex-1-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 1.1<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-1-real-numbers-ex-1-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 1.2<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-1-real-numbers-ex-1-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 1.3<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 1.4\u00a0<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. 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:<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6133\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q1.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"718\" height=\"184\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q1.png 718w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q1-300x77.png 300w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/span><br \/>\n<span style=\"color: #000000;\"><strong>Solutions &#8211;<br \/>\n<\/strong><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{13}{3125}}\" alt=\"\\mathbf{\\frac{13}{3125}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Factorizing the denominator, we get,<br \/>\n3125 = 5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 5 = 5<sup>5<br \/>\n<\/sup>The denominator is of the form 5<sup><i>m<\/i><\/sup>.<\/span><br \/>\n<span style=\"color: #000000;\">Hence, the decimal expansion of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{13}{3125}\" alt=\"\\frac{13}{3125}\" align=\"absmiddle\" \/> is terminating.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{17}{8}}\" alt=\"\\mathbf{\\frac{17}{8}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Factorizing the denominator, we get,<br \/>\n8 = 2 \u00d7 2 \u00d7 2 = 2<sup>3<br \/>\n<\/sup>The denominator is of the form 2<sup><i>m<\/i><\/sup>.<br \/>\nHence, the decimal expansion of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{17}{8}\" alt=\"\\frac{17}{8}\" align=\"absmiddle\" \/>\u00a0is terminating.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{64}{455}}\" alt=\"\\mathbf{\\frac{64}{455}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Factorizing the denominator, we get,<br \/>\n455 = 5 \u00d7 7 \u00d7 13<br \/>\nSince, the denominator is not in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup>, thus <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{64}{455}\" alt=\"\\frac{64}{455}\" align=\"absmiddle\" \/> has a non-terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{15}{1600}}\" alt=\"\\mathbf{\\frac{15}{1600}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Factorizing the denominator, we get,<br \/>\n1600 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<sup>\u00a0<\/sup>\u00d7 5 \u00d7 5 = 2<sup>6 <\/sup>\u00d7 5<sup>2<br \/>\n<\/sup>Since, the denominator is in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup>, thus <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{1600}\" alt=\"\\frac{15}{1600}\" align=\"absmiddle\" \/> has a terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{29}{343}}\" alt=\"\\mathbf{\\frac{29}{343}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Factorizing the denominator, we get,<br \/>\n343 = 7 \u00d7 7 \u00d7 7 = 7<sup>3<\/sup><br \/>\nSince, the denominator is not in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup> thus <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{29}{343}\" alt=\"\\frac{29}{343}\" align=\"absmiddle\" \/>\u00a0 has a non-terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{23}{2^3&amp;space;5^2}}\" alt=\"\\mathbf{\\frac{23}{2^3 5^2}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Clearly, the denominator is in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup>.<br \/>\nHence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{23}{2^3&amp;space;5^2}\" alt=\"\\frac{23}{2^3 5^2}\" align=\"absmiddle\" \/> \u00a0has a terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{129}{2^5&amp;space;5^7&amp;space;7^5}}\" alt=\"\\mathbf{\\frac{129}{2^5 5^7 7^5}}\" width=\"56\" height=\"37\" align=\"absmiddle\" \/><br \/>\n<\/strong>As you can see, the denominator is not in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup>.<br \/>\nHence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{129}{2^5&amp;space;5^7&amp;space;7^5}\" alt=\"\\frac{129}{2^5 5^7 7^5}\" align=\"absmiddle\" \/> \u00a0has a non-terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(viii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{6}{15}}\" alt=\"\\mathbf{\\frac{6}{15}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{15}&amp;space;=&amp;space;\\frac{2}{5}\" alt=\"\\frac{6}{15} = \\frac{2}{5}\" align=\"absmiddle\" \/><br \/>\nSince, the denominator has only 5 as its factor, thus, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{15}\" alt=\"\\frac{6}{15}\" align=\"absmiddle\" \/> has a terminating decimal expansion.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ix) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{35}{50}}\" alt=\"\\mathbf{\\frac{35}{50}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{35}{50}&amp;space;=&amp;space;\\frac{7}{10}\" alt=\"\\frac{35}{50} = \\frac{7}{10}\" align=\"absmiddle\" \/><br \/>\nFactorising the denominator, we get,<br \/>\n10 = 2 \u00d7 5<br \/>\nSince, the denominator is in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup> thus, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{35}{50}\" alt=\"\\frac{35}{50}\" align=\"absmiddle\" \/>\u00a0 has a terminating decimal expansion.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(x) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{77}{210}}\" alt=\"\\mathbf{\\frac{77}{210}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{77}{210}\" alt=\"\\frac{77}{210}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{30}\" alt=\"\\frac{11}{30}\" align=\"absmiddle\" \/><br \/>\nFactorising the denominator, we get,<br \/>\n30 = 2 \u00d7 3 \u00d7 5<br \/>\nAs you can see, the denominator is not in the form of 2<sup>m<\/sup> \u00d7 5<sup>n<\/sup>.<br \/>\nHence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{77}{210}\" alt=\"\\frac{77}{210}\" align=\"absmiddle\" \/> has a non-terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.<br \/>\n<\/strong><strong>Solutions &#8211;<br \/>\n<\/strong><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{13}{3125}}\" alt=\"\\mathbf{\\frac{13}{3125}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6134\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2i.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"114\" height=\"341\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2i.png 114w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2i-100x300.png 100w\" sizes=\"auto, (max-width: 114px) 100vw, 114px\" \/><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{13}{3125}\" alt=\"\\frac{13}{3125}\" align=\"absmiddle\" \/>\u00a0 = 0.00416\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{17}{8}}\" alt=\"\\mathbf{\\frac{17}{8}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6135\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2ii.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"92\" height=\"245\" \/><br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{17}{8}\" alt=\"\\frac{17}{8}\" align=\"absmiddle\" \/> = 2.125<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{64}{455}}\" alt=\"\\mathbf{\\frac{64}{455}}\" align=\"absmiddle\" \/> <\/strong>has a non terminating decimal expansion<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{15}{1600}}\" alt=\"\\mathbf{\\frac{15}{1600}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6138\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2vi.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"126\" height=\"393\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2vi.png 126w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2vi-96x300.png 96w\" sizes=\"auto, (max-width: 126px) 100vw, 126px\" \/><\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{1600}\" alt=\"\\frac{15}{1600}\" align=\"absmiddle\" \/> = 0.009375<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{29}{343}}\" alt=\"\\mathbf{\\frac{29}{343}}\" align=\"absmiddle\" \/> <\/strong>has a non terminating decimal expansion<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{23}{2^3&amp;space;5^2}}\" alt=\"\\mathbf{\\frac{23}{2^3 5^2}}\" align=\"absmiddle\" \/> <\/strong>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{23}{8\\times&amp;space;25}&amp;space;=&amp;space;\\frac{23}{200}\" alt=\"\\frac{23}{8\\times 25} = \\frac{23}{200}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6140\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2-vi.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"92\" height=\"240\" \/><\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{23}{2^3&amp;space;5^2}\" alt=\"\\frac{23}{2^3 5^2}\" align=\"absmiddle\" \/>\u00a0 = 0.115<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{129}{2^5&amp;space;5^7&amp;space;7^5}}\" alt=\"\\mathbf{\\frac{129}{2^5 5^7 7^5}}\" width=\"56\" height=\"37\" align=\"absmiddle\" \/> <\/strong>has a non terminating decimal expansion<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(viii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{6}{15}}\" alt=\"\\mathbf{\\frac{6}{15}}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6139\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2viii.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"40\" height=\"147\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/> = 0.4\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ix) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{35}{50}}\" alt=\"\\mathbf{\\frac{35}{50}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6137\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex1.4-Q2ix.png\" alt=\"NCERT Class 10 Maths Solution \" width=\"60\" height=\"144\" \/><\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" style=\"text-align: justify;\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{35}{50}\" alt=\"\\frac{35}{50}\" align=\"absmiddle\" \/> <span style=\"text-align: justify;\">= 0.7<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(x) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{77}{210}}\" alt=\"\\mathbf{\\frac{77}{210}}\" align=\"absmiddle\" \/>\u00a0<\/strong> has a non-terminating decimal expansion.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. The 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, p q what can you say about the prime factors of q?<br \/>\n<\/strong><strong>(i) 43.123456789<br \/>\n<\/strong><strong>(ii) 0.120120012000120000. . .<br \/>\n<\/strong><strong>(iii) 43.<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\overline{123456789}}\" alt=\"\\mathbf{\\overline{123456789}}\" align=\"absmiddle\" \/>\u00a0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211; <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) 43.123456789<br \/>\n<\/strong>Since it has a terminating decimal expansion, it is a rational number in the form of p\/q and q has factors of 2 and 5 only.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 0.120120012000120000 . . .<br \/>\n<\/strong>Since, it has non-terminating and non- repeating decimal expansion, it is an irrational number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 43.<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\overline{123456789}}\" alt=\"\\mathbf{\\overline{123456789}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Since it has non-terminating but repeating decimal expansion, it is a rational number in the form of p\/q and q has factors other than 2 and 5.<\/span><\/p>\n<p><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\"><span style=\"color: #0000ff;\"><b><i>Go Back To Chapters<\/i><\/b><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 1 (Real Numbers)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 1 Real Numbers\u00a0 Exercise 1.4 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 1 Real Numbers NCERT Class 10 Maths Solution Ex &#8211; 1.1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1046,1052,1044,1049,1048],"class_list":["post-6005","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-1-real-numbers-solutions","tag-ncert-class-10-mathematics-exercise-1-4-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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