{"id":34520,"date":"2020-07-11T12:00:39","date_gmt":"2020-07-11T06:30:39","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=34520"},"modified":"2020-11-27T11:49:25","modified_gmt":"2020-11-27T06:19:25","slug":"ncert-solutions-for-class-10-maths-chapter-1-ex-1-4","status":"publish","type":"post","link":"https:\/\/cbselibrary.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":"<p>NCERT Maths Solutions for <a href=\"https:\/\/ncertlibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-4\/\">Ex 1.4 Class 10<\/a> Real Numbers is the perfect guide to boost up your preparation during CBSE 10th Class Maths Examination.<\/p>\n<p>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 are part of <a class=\"button-red\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths\/\">NCERT Solutions for Class 10 Maths<\/a>. Here are we have given Chapter 1\u00a0<strong>Real Numbers Class 10 NCERT Solutions Ex 1.4.\u00a0<\/strong><\/p>\n<ul>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.1<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-2\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.2<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-3\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.3<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-4\/\" target=\"_blank\" rel=\"noopener\">Real Numbers Class 10 Ex 1.4<\/a><\/li>\n<\/ul>\n<table style=\"table-layout: fixed; width: 650px;\" border=\"1\">\n<tbody>\n<tr>\n<td><strong>Board<\/strong><\/td>\n<td>CBSE<\/td>\n<\/tr>\n<tr>\n<td><strong>Textbook<\/strong><\/td>\n<td>NCERT<\/td>\n<\/tr>\n<tr>\n<td><strong>Class<\/strong><\/td>\n<td>Class 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Subject<\/strong><\/td>\n<td>Maths<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter<\/strong><\/td>\n<td>Chapter 1<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter Name<\/strong><\/td>\n<td>Real Numbers<\/td>\n<\/tr>\n<tr>\n<td><strong>Exercise<\/strong><\/td>\n<td>Ex 1.4<\/td>\n<\/tr>\n<tr>\n<td><strong>Number of Questions Solved<\/strong><\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><strong>Category<\/strong><\/td>\n<td>NCERT Solutions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4<\/h2>\n<p>Page No: 17<\/p>\n<p><strong><b>Question 1<\/b><\/strong><br \/>\nWithout actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal\u00a0expansion:<br \/>\n(i) 13\/3125<br \/>\n(ii) 17\/8<br \/>\n(iii) 64\/455<br \/>\n(iv) 15\/1600<br \/>\n(v) 29\/343<br \/>\n(vi) 23\/2<sup>3 <\/sup>\u00d7 5<sup>2<br \/>\n<\/sup>(vii) 129\/2<sup>2 <\/sup>\u00d7 5<sup>7 <\/sup>\u00d7 7<sup>5<br \/>\n<\/sup>(viii) 6\/15<br \/>\n(ix) 35\/50<br \/>\n(x) 77\/210<\/p>\n<div>\n<p><strong>Solution:<\/strong><\/p>\n<\/div>\n<div>\n<div class=\"table-responsive\">\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-98754\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-17.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 17\" width=\"87\" height=\"44\" \/><br \/>\n3125 = 5<sup><sub>5<\/sub><\/sup><br \/>\nThe denominator is of the form 5<sup>m<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98756\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-17i.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 17(i)\" width=\"364\" height=\"79\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-17i.png 364w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-17i-300x65.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><br \/>\n8 = 2<sup>3<\/sup><br \/>\nThe denominator is of the form 2<sup>m<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98961\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-19.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 19\" width=\"329\" height=\"86\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-19.jpg 329w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-19-300x78.jpg 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\n455 = 5 x 7 x 13<br \/>\nSince the denominator is not in the form 2<sup><sub>m<\/sub><\/sup>\u00a0x 5<sup><sub>n<\/sub><\/sup>, and it also contains 7 and 13 as its factors, its decimal expansion will be non-terminating repeating.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99089\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-20.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 20\" width=\"86\" height=\"42\" \/><br \/>\n1600 = 2<sup><sub>6<\/sub><\/sup> \u00d7\u00a05<sup><sub>2<\/sub><\/sup><br \/>\nThe denominator is of the form 2<sup><sub>m<\/sub><\/sup>\u00a0x 5<sup><sub>n<\/sub><\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99091\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-21.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 21\" width=\"348\" height=\"36\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-21.jpg 348w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-21-300x31.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99094\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-22.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 22\" width=\"77\" height=\"36\" \/><br \/>\n343 = 7<sup><sub>3<\/sub><\/sup><br \/>\nSince the denominator is not in the form 2<sup><sub>m<\/sub><\/sup>\u00a0x 5<sup><sub>n<\/sub><\/sup>, and it has 7 as its factor,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99097\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-23.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 23\" width=\"389\" height=\"69\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-23.jpg 389w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-23-300x53.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\nThe denominator is of the form 2<sup><sub>m<\/sub><\/sup>\u00a0x 5<sup><sub>n<\/sub><\/sup>. Hence, the decimal expansion of is <img loading=\"lazy\" class=\"alignnone size-full wp-image-99100\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-24.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 24\" width=\"46\" height=\"30\" \/>\u00a0terminating.<\/p>\n<p>(vii)<img loading=\"lazy\" class=\"alignnone  wp-image-99026\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-25.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 25\" width=\"96\" height=\"44\" \/><br \/>\nSince the denominator is not of the form 2<sup>m<\/sup>\u00a0\u00a05<sup>n<\/sup>, and it also has 7 as its<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99029\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-26.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 26\" width=\"482\" height=\"89\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-26.jpg 482w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-26-300x55.jpg 300w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nThe denominator is of the form 5<sup><sub>n<\/sub><\/sup>.<br \/>\n10 = 2 x 5<br \/>\nThe denominator is of the form 2<sup><sub>m<\/sub><\/sup>\u00a0x 5<sup><sub>n<\/sub><\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99037\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-27.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 27\" width=\"339\" height=\"89\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-27.jpg 339w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-27-300x79.jpg 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><br \/>\n30 = 2 x 3 x 5<br \/>\nSince the denominator is not of the form 2<sup>m<\/sup> \u00d7\u00a05<sup>n<\/sup>, and it also has 3 as its factors,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-99083\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-28.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 28\" width=\"390\" height=\"35\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-28.jpg 390w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-28-300x27.jpg 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Concept Insight: The concept used in this problem is that The decimal expansion of rational number p\/q\u00a0where p and q are coprime numbers, terminates if and only if the prime factorization of q is of the form 2<sup>n<\/sup>5<sup>m<\/sup>, where n and m are non negative integers. Do not forget that 0 is also a non negative integer so n or m can take value 0.<br \/>\nGenerally, mistake is committed in identifying terminating decimals when either of the two prime numbers\u00a0 2 or 5 is appearing in the prime factorization.<\/p>\n<\/div>\n<p>Page No: 18<\/p>\n<p><strong><b>Question 2<\/b><\/strong><br \/>\nWrite down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.<\/p>\n<\/div>\n<p><strong>Solution:<\/strong><\/p>\n<div class=\"table-responsive\">\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-98933\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-29.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 29\" width=\"372\" height=\"819\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-29.jpg 372w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-29-136x300.jpg 136w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-98953\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-30.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers 30\" width=\"359\" height=\"463\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-30.jpg 359w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2020\/07\/NCERT-Solutions-for-Class-10-Maths-Chapter-1-Real-Numbers-30-233x300.jpg 233w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p><strong>Concept Insight:<br \/>\n<\/strong>This is based on performing the long division and expressing the rational number in the decimal form learned in lower classes.<\/p>\n<\/div>\n<p><strong><b>Question 3<\/b><\/strong><br \/>\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 p, <i>q<\/i> you say about the prime factors of\u00a0<i>q<\/i>?<br \/>\n(i) 43.123456789<br \/>\n(ii) 0.120120012000120000\u2026<br \/>\n(iii) 43.123456789<\/p>\n<div style=\"text-align: justify;\">\n<p><strong>Solution:<br \/>\n<\/strong>(i) 43.123456789<strong><br \/>\n<\/strong>Since this number has a terminating decimal expansion, it is a rational number of the form\u00a0 p\\q\u00a0and q is of the form 2<sup>m<\/sup>\u00a0x 5<sup>n<\/sup>,<br \/>\ni.e., the prime factors of q will be either 2 or 5 or both.<\/p>\n<div class=\"FL col-lg-8 col-md-8 col-xs-12 col1-2\">\n<div class=\"tbkcontWrap\">\n<div id=\"ex__1_4\">\n<div class=\"solnBox\">\n<div class=\"table-responsive\">\n<p>(ii) 0.120120012000120000&#8230;<br \/>\nThe decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number.<\/p>\n<p>(iii) 43.123456789<br \/>\nSince the decimal expansion is non-terminating recurring, the given number is a rational number of the form p\/q and q is not of the form 2<sup><sub>m<\/sub><\/sup>\u00a0x 5<sup><sub>n<\/sub><\/sup>\u00a0 i.e., the prime factors of q will also have a\u00a0factor other than 2 or 5.<\/p>\n<p>Concept Insight:\u00a0The concept used in this problem is that,\u00a0If the decimal expansion of rational number p\\q, [where p and q are coprime numbers] terminates,\u00a0then prime factorization\u00a0of q is of the form 2<sup>n<\/sup>5<sup>m<\/sup>, where n and m are non negative integers.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>We hope the NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Maths Solutions for Ex 1.4 Class 10 Real Numbers is the perfect guide to boost up your preparation during CBSE 10th Class Maths Examination. NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 1\u00a0Real Numbers Class &#8230; <a title=\"NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/ncert-solutions-for-class-10-maths-chapter-1-ex-1-4\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4\">Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[36685],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4 - AplusTopper.com<\/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:\/\/cbselibrary.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\" \/>\n<meta property=\"og:description\" content=\"NCERT Maths Solutions for Ex 1.4 Class 10 Real Numbers is the perfect guide to boost up your preparation during CBSE 10th Class Maths Examination. 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