{"id":5085,"date":"2023-10-31T11:10:31","date_gmt":"2023-10-31T05:40:31","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=5085"},"modified":"2023-11-01T10:09:50","modified_gmt":"2023-11-01T04:39:50","slug":"ap-ssc-10th-class-maths-solutions-chapter-1-ex-1-3","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-ssc-10th-class-maths-solutions-chapter-1-ex-1-3\/","title":{"rendered":"AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.3"},"content":{"rendered":"

AP State Board Syllabus\u00a0AP SSC 10th Class Maths Textbook Solutions<\/a> Chapter 1 Real Numbers Ex 1.3 Textbook Questions and Answers.<\/p>\n

AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.3<\/h2>\n

10th Class Maths 1st Lesson Real Numbers Ex 1.3 Textbook Questions<\/h3>\n

Question 1.
\nWrite the following rational numbers in their decimal form and also state which are terminating and which have non-terminating repeating decimals.
\ni) \\(\\frac{3}{8}\\)
\nii) \\(\\frac{229}{400}\\)
\niii) 4\\(\\frac{1}{5}\\)
\niv) \\(\\frac{2}{11}\\)
\nv) \\(\\frac{8}{125}\\)
\nAnswer:
\ni) \\(\\frac{3}{8}\\)
\n\"AP
\n[!! Denominator 8 = 23<\/sup>, consists of only 2\u2019s. Hence a terminating decimal.]
\n\u2234 \\(\\frac{3}{8}\\) = 0.375 is a terminating decimal.<\/p>\n

\"AP<\/p>\n

ii) \\(\\frac{229}{400}\\)
\n\"AP
\n[!! Denominator 400 = 24<\/sup> \u00d7 52<\/sup> = 2n<\/sup> \u00d7 5m<\/sup>. Hence a terminating decimal.]
\n\u2234 \\(\\frac{229}{400}\\) = 0.5725 is a terminating decimal.<\/p>\n

iii) 4\\(\\frac{1}{5}\\)
\n4\\(\\frac{1}{5}\\) = 4 + \\(\\frac{1}{5}\\)
\n\"AP
\n[!! Denominator is 5. Hence a terminating decimal.]
\n\u2234 4\\(\\frac{1}{5}\\) = 4.2 is a terminating decimal.<\/p>\n

iv) \\(\\frac{2}{11}\\)
\n\"AP
\n[!! Denominator is not of the form 2m<\/sup> \u00d7 5n<\/sup>. Hence a non-terminating repeating decimal.]
\n\u2234 \\(\\frac{2}{11}\\) = \\(0 . \\overline{18}\\) is a non terminating, repeating decimal.<\/p>\n

\"AP<\/p>\n

v) \\(\\frac{8}{125}\\)
\n\"AP
\n[!! Denominator 125 = 53<\/sup>. Hence a terminating decimal.]
\n\u2234 \\(\\frac{8}{125}\\) = 0.064 is a terminating decimal.<\/p>\n

Question 2.
\nWithout performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form.
\ni) \\(\\frac{13}{3125}\\)
\nii) \\(\\frac{11}{12}\\)
\niii) \\(\\frac{64}{455}\\)
\niv) \\(\\frac{15}{1600}\\)
\nv) \\(\\frac{29}{343}\\)
\nvi) \\(\\frac{23}{2^{3} \\cdot 5^{2}}\\)
\nvii) \\(\\frac{129}{2^{2} \\cdot 5^{7} \\cdot 7^{5}}\\)
\nviii) \\(\\frac{9}{15}\\)
\niX) \\(\\frac{36}{100}\\)
\nX) \\(\\frac{77}{210}\\)
\nAnswer:
\ni) \\(\\frac{13}{3125}\\)
\nNote: We check whether the denominator is of the form 2n<\/sup> . 5m<\/sup> or not? If yes, the rational number can be expressed as a terminating decimal. If not, it can’t be expressed as a terminating decimal.
\n\"AP
\n[!! Denominator is of the form 2m<\/sup> \u00d7 5n<\/sup>. Hence a terminating decimal.]
\n3125 = 55<\/sup>
\n\u2234 \\(\\frac{13}{3125}\\) is a terminating decimal.<\/p>\n

ii) \\(\\frac{11}{12}\\)
\nThe denominator 12 is not a factor of 11. Moreover 12 = 22<\/sup> \u00d7 3.
\n[!! Denominator is not of the form 2m<\/sup> \u00d7 5n<\/sup>.]
\n\u2234 \\(\\frac{11}{12}\\) is a non terminating, repeating decimal.<\/p>\n

\"AP<\/p>\n

iii) \\(\\frac{64}{455}\\)
\n\"AP
\n[!! Denominator is not of the form 2m<\/sup> \u00d7 5n<\/sup>. Hence a non terminating decimal.]
\n\u2234 455 = 5 \u00d7 7 \u00d7 13
\nHence\\(\\frac{64}{455}\\) is a non terminating, repeating decimal.<\/p>\n

iv) \\(\\frac{15}{1600}\\)
\n\"AP
\n\u2234 1600 = 26<\/sup> \u00d7 52<\/sup> [\u2235 The denominator is of the form 2n<\/sup> . 5m<\/sup>]
\nHence \\(\\frac{15}{1600}\\) is a terminating decimal.<\/p>\n

v) \\(\\frac{29}{343}\\)
\n\"AP
\n343 = 73<\/sup> [Not of the form 2n<\/sup> . 5m<\/sup>]
\n\u2234 \\(\\frac{29}{343}\\) is a non terminating, repeating decimal.<\/p>\n

vi) \\(\\frac{23}{2^{3} \\cdot 5^{2}}\\)
\n\\(\\frac{23}{2^{3} \\cdot 5^{2}}\\) is a terminating decimal.
\n[\u2235 The denominator is of the form 2n<\/sup> . 5m<\/sup>]<\/p>\n

vii) \\(\\frac{129}{2^{2} \\cdot 5^{7} \\cdot 7^{5}}\\)
\n\\(\\frac{129}{2^{2} \\cdot 5^{7} \\cdot 7^{5}}\\) is a non terminating, repeating decimal.<\/p>\n

viii) \\(\\frac{9}{15}\\)
\n\\(\\frac{9}{15}\\) = \\(\\frac{3}{5}\\)
\nDenominator is of the form 2n<\/sup> . 5m<\/sup>.
\n\u2234 \\(\\frac{9}{15}\\) = \\(\\frac{3}{5}\\) is a terminating decimal.<\/p>\n

ix) \\(\\frac{36}{100}\\)
\n100 = 22<\/sup> \u00d7 52<\/sup> is of the form 2n<\/sup> . 5m<\/sup>
\nHence \\(\\frac{36}{100}\\) is a terminating decimal.<\/p>\n

\"AP<\/p>\n

x) \\(\\frac{77}{210}\\)
\n\"AP
\n210 = 2 \u00d7 3 \u00d7 5 \u00d7 7 is not of the form 2n<\/sup> . 5m<\/sup>
\nGiven fraction has a non-terminating, repeating decimal expansion.<\/p>\n

Question 3.
\nWrite the following rationals in decimal form using Theorem 1.4.
\ni) \\(\\frac{13}{25}\\)
\nii) \\(\\frac{15}{16}\\)
\niii) \\(\\frac{23}{2^{3} \\cdot 5^{2}}\\)
\niv) \\(\\frac{7218}{3^{2} \\cdot 5^{2}}\\)
\nv) \\(\\frac{143}{110}\\)
\nAnswer:
\ni) \\(\\frac{13}{25}\\)
\n\"AP<\/p>\n

ii) \\(\\frac{15}{16}\\)
\n\\(\\frac{15}{16}\\) = \\(\\frac{15}{2 \\times 2 \\times 2 \\times 2}\\)
\n\"AP<\/p>\n

iii) \\(\\frac{23}{2^{3} \\cdot 5^{2}}\\)
\n\"AP<\/p>\n

\"AP<\/p>\n

iv) \\(\\frac{7218}{3^{2} \\cdot 5^{2}}\\)
\n\"AP<\/p>\n

v) \\(\\frac{143}{110}\\)
\n\"AP<\/p>\n

Question 4.
\nThe decimal form of some real numbers are given below. In each case, decide whether the number is rational or not. If it is rational, and expressed in form p\/q, what can you say about the prime factors of q?
\ni) 43.12345678?
\nii) 0.120120012000120000 ……….
\niii) \\(43 . \\overline{123456789}\\)
\nAnswer:
\ni) 43.123456789
\nThe given decimal expansion is terminating. Hence it is a rational number and the denominator q is of the form 2n<\/sup> . 5m<\/sup>.<\/p>\n

\"AP<\/p>\n

ii) 0.120120012000120000 …………
\nThe given decimal expansion is neither terminating nor repeating.
\nHence it is not a rational number. It represents an irrational number.<\/p>\n

iii) \\(43 . \\overline{123456789}\\)
\nThe given real number is a repeating decimal with period 123456789. Hence it is a rational number.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Board Syllabus\u00a0AP SSC 10th Class Maths Textbook Solutions Chapter 1 Real Numbers Ex 1.3 Textbook Questions and Answers. AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.3 10th Class Maths 1st Lesson Real Numbers Ex 1.3 Textbook Questions Question 1. Write the following rational numbers in their decimal … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/5085"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=5085"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/5085\/revisions"}],"predecessor-version":[{"id":33978,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/5085\/revisions\/33978"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=5085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=5085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=5085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}