{"id":162,"date":"2025-01-06T11:00:41","date_gmt":"2025-01-06T05:30:41","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=162"},"modified":"2025-01-07T10:09:37","modified_gmt":"2025-01-07T04:39:37","slug":"samacheer-kalvi-9th-maths-guide-chapter-2-ex-2-2","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-9th-maths-guide-chapter-2-ex-2-2\/","title":{"rendered":"Samacheer Kalvi 9th Maths Guide Chapter 2 Real Numbers Ex 2.2"},"content":{"rendered":"

Students can download Maths Chapter 2 Real Numbers Ex 2.2 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide<\/a> Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.<\/p>\n

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.2<\/h2>\n

Therefore, one Decimal<\/a> is equal to four hundred and thirty five decimal point six Square Feet (sq ft) in Online.<\/p>\n

Question 1.
\nExpress the following rational numbers into decimal and state the kind of decimal expression.
\n(i) \\(\\frac{2}{7}\\)
\n(ii) -5\\(\\frac{3}{11}\\)
\n(iii) \\(\\frac{22}{3}\\)
\n(iv) \\(\\frac{327}{200}\\)
\nSolution:
\n\"Samacheer
\n(i) \\(\\frac{2}{7}\\) = 0.2857142….
\n= 0.\\(\\overline {285714}\\)
\nNon-terminating and recurring decimal expansion.<\/p>\n

\"Samacheer<\/p>\n

(ii) -5\\(\\frac{3}{11}\\) = -5 + 0.272 = -5.272……..
\n\"Samacheer
\n= -5.\\(\\overline {27}\\)
\nNon-terminating and recurring decimal expansion.<\/p>\n

(iii) \\(\\frac{22}{3}\\) = 7.333……..
\n\"Samacheer
\n= 7.\\(\\overline {3}\\)
\nNon-terminating and recurring decimal expansion.<\/p>\n

(iv) \\(\\frac{327}{200}\\) = \\(\\frac{327}{2\u00d7100}\\)
\n\"Samacheer
\n= \\(\\frac{3.27}{2}\\)
\n= 1.635
\nTerminating decimal expansion.<\/p>\n

\"Samacheer<\/p>\n

How to convert 1\/32 to decimal<\/a> form? … In the fraction 1\/32, 1 is the numerator and 32 is the denominator, the fraction bar means “divided by”.<\/p>\n

Question 2.
\nExpress \\(\\frac{1}{13}\\) in decimal form. Find the length of the period of decimals.
\nSolution:
\n\"Samacheer
\n\\(\\frac{1}{13}\\) = 0.07692307
\n= 0.\\(\\overline {076923}\\)
\nLength of the period of decimal is 6.<\/p>\n

9\/20 as a decimal<\/a> is 0.45<\/p>\n

Question 3.
\nExpress the rational number \\(\\frac{1}{33}\\) in recurring decimal form by using the recurring decimal expansion of \\(\\frac{1}{11}\\). Hence write \\(\\frac{71}{33}\\) in recurring decimal form.
\nSolution:
\n\"Samacheer
\n\\(\\frac{1}{11}\\) = 0.0909……… = 0.\\(\\overline {09}\\)
\n\u2234 \\(\\frac{1}{33}\\) = \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{11}\\)
\n= \\(\\frac{1}{3}\\) \u00d7 0.0909 ……..
\n= 0.0303 …… = 0.\\(\\overline {03}\\)
\n\\(\\frac{71}{33}\\) = 2\\(\\frac{5}{33}\\) = 2 + \\(\\frac{5}{33}\\) = 2 + 5 \u00d7 \\(\\frac{1}{33}\\)
\n= 2 + 5 \u00d7 0.\\(\\overline {03}\\)
\n2 + (5 \u00d7 0.030303 ……..)
\n2 + 0.151515 ………
\n2+ 0.\\(\\overline {15}\\)
\n2.\\(\\overline {15}\\)<\/p>\n

That’s literally all there is to it! 1\/2 as a decimal<\/a> is 0.5.<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nExpress the following decimal expression into rational numbers.
\n(i) 0.24
\nSolution:
\nLet x = 0.242424 ………. \u2192(1)
\n100 x = 24.2424 ……… \u2192(2)
\n(2) – (1) \u21d2 100 x – x = 24.2424 ……….. (-)
\n\u00a00.2424<\/span> ……..
\n99 x = 24.0000
\nx = \\(\\frac{24}{99}\\)
\n(or)
\n\\(\\frac{8}{33}\\)<\/p>\n

(ii) 2.327
\nSolution:
\nLet x = 2.327327327 ………. \u2192(1)
\n1000 x = 2327.327327 ……… \u2192(2)
\n(2) – (1) \u21d2 1000 x – x = 2327.327327 ……….. (-)
\n\u00a0 2.327327<\/span> ……..
\n999 x = 2325.000
\nx = \\(\\frac{2325}{999}\\)
\n(or)
\n\\(\\frac{775}{333}\\)<\/p>\n

\"Samacheer<\/p>\n

3\/5 as a decimal<\/a>\u00a0is 0.6<\/p>\n

(iii) – 5.132
\nSolution:
\n– 5.132 = -5 + \\(\\frac{1}{10}\\) + \\(\\frac{3}{100}\\) + \\(\\frac{2}{1000}\\)
\n= \\(\\frac{-5000 + 100 +30 + 2}{1000}\\) = \\(\\frac{-4868}{1000}\\)
\n(or)
\n\\(\\frac{-1217}{250}\\)<\/p>\n

(iv) 3.17
\nSolution:
\nLet x = 3.1777 ………. \u2192(1)
\n10 x = 31.777 ……… \u2192(2)
\n100 x = 317.77 …….. \u2192(3)
\n(3) – (2) \u21d2 100 x – 10 x = 317.77 ……….. (-)
\n\u00a031.777<\/span> ……..
\n90 x = 286.000
\nx = \\(\\frac{286}{90}\\)
\n(or)
\n\\(\\frac{143}{45}\\)<\/p>\n

(v) 17.215
\nSolution:
\nLet x = 17.2151515 ………. \u2192(1)
\n10 x = 172.151515 ……… \u2192(2)
\n100 x = 17215.1515 …….. \u2192(3)
\n(3) – (2) \u21d2 1000 x – 10 x = 17215.1515 ……….. (-)
\n\u00a017215.1515<\/span> ……..
\n990 x = 17043
\nx = \\(\\frac{17043}{990}\\)
\n(or)
\n\\(\\frac{5681}{330}\\)<\/p>\n

\"Samacheer<\/p>\n

(vi) -21.2137
\nSolution:
\nLet x = -21.213777 ………. \u2192(1)
\n1000 x = -21213.777 ……… \u2192(2)
\n100 x = -212137.77 …….. \u2192(3)
\n(3) – (2) \u21d2 10000 x – 1000 x = -21213.777 ……….. (-)
\n-21213.777 ……..
\n9000 x = -190924
\nx = \\(\\frac{-190924}{9000}\\)
\n(or)
\n\\(\\frac{-47731}{2250}\\)<\/p>\n

That’s literally all there is to it! 11\/16 as a decimal<\/a> is 0.6875.<\/p>\n

Question 5.
\nWithout actual division, find which of the following rational numbers have terminating decimal expression.
\n(i) \\(\\frac{7}{128}\\)
\nSolution:
\n\"Samacheer
\n\\(\\frac{7}{128}\\) = \\(\\frac{7}{2^{7}}\\)
\n\u2234 \\(\\frac{7}{128}\\) has terminating decimal expression.<\/p>\n

\"Samacheer<\/p>\n

(ii) \\(\\frac{21}{15}\\)
\nSolution:
\n\\(\\frac{21}{15}\\) = \\(\\frac{7}{5}\\) = \\(\\frac{7}{5^1}\\)
\n\\(\\frac{21}{15}\\) has terminating decimal expression.<\/p>\n

(iii) 4\\(\\frac{9}{35}\\)
\nSolution:
\n4\\(\\frac{9}{35}\\) = \\(\\frac{149}{35}\\)
\n4\\(\\frac{149}{5\u00d77}\\) (It is not in the form of \\(\\frac{P}{2^{m} \u00d7 5^{n}}\\)
\n\u2234 4\\(\\frac{9}{35}\\) has non-terminating recurring decimal expression.<\/p>\n

(iv) \\(\\frac{219}{2200}\\)
\nSolution:
\n\"Samacheer
\n\\(\\frac{219}{2200}\\) = \\(\\frac{219}{2^{3} \u00d7 5^{2} \u00d7 11}\\) (It is not in the form of \\(\\frac{P}{2^{m} \u00d7 5^{n}}\\)
\n\u2234 \\(\\frac{219}{2200}\\) has non-terminating recurring decimal expression.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can download Maths Chapter 2 Real Numbers Ex 2.2 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex …<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[],"class_list":["post-162","post","type-post","status-publish","format-standard","hentry","category-class-9"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/162"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=162"}],"version-history":[{"count":8,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/162\/revisions"}],"predecessor-version":[{"id":39701,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/162\/revisions\/39701"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}