{"id":268,"date":"2023-10-20T12:51:59","date_gmt":"2023-10-20T07:21:59","guid":{"rendered":"https:\/\/samacheer-kalvi.com\/?p=268"},"modified":"2023-11-10T10:37:57","modified_gmt":"2023-11-10T05:07:57","slug":"samacheer-kalvi-9th-maths-guide-chapter-2-additional-questions","status":"publish","type":"post","link":"https:\/\/samacheer-kalvi.com\/samacheer-kalvi-9th-maths-guide-chapter-2-additional-questions\/","title":{"rendered":"Samacheer Kalvi 9th Maths Guide Chapter 2 Real Numbers Additional Questions"},"content":{"rendered":"

Students can download Maths Chapter 2 Real Numbers Additional 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 Additional Questions<\/h2>\n

I. Multiple choice question<\/p>\n

Question 1.
\nThe decimal form of –\\(\\frac{3}{4}\\) is ………
\n(a) – 0.75
\n(b) – 0.50
\n(c) – 0.25
\n(d) – 0.125
\nSolution:
\n(a) – 0.75<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nIf a number has a non-terminating and non-recurring decimal expansion, then it is……….
\n(a) a rational number
\n(b) a natural number
\n(c) an irrational number
\n(d) an integer
\nSolution:
\n(c) an irrational number<\/p>\n

Question 3.
\nWhich one of the following has terminating decimal expansion?
\n(a) \\(\\frac{7}{9}\\)
\n(b) \\(\\frac{8}{15}\\)
\n(c) \\(\\frac{1}{12}\\)
\n(d) \\(\\frac{5}{32}\\)
\nSolution:
\n(d) \\(\\frac{5}{32}\\)<\/p>\n

Question 4.
\nWhich of the following are irrational numbers?
\n(i) \\(\\sqrt{2+\\sqrt3}\\)
\n(ii) \\(\\sqrt{4+\\sqrt25}\\)
\n(iii) \\(\\sqrt[3]{5+\\sqrt7}\\)
\n(iv) \\(\\sqrt{8-\\sqrt[3]8}\\)
\n(a) (ii), (iii) and (iv)
\n(b) (i), (iii) and (iv)
\n(c) (i), (ii) and (iii)
\n(d) (i), (iii) and (iv)
\nSolution:
\n(d) (i), (iii) and (iv)<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nIrrational number has a
\n(a) terminating decimal
\n(b) no decimal part
\n(c) non-terminating and recurring decimal
\n(d) non-terminating and non-recurring decimal
\nSolution:
\n(d) non-terminating and non-recurring decimal<\/p>\n

Question 6.
\nIf \\(\\frac{1}{7}\\) = 0.142857, then the value of \\(\\frac{3}{7}\\) is……..
\n(a) 0.285741
\n(b) 0.428571
\n(c) 0.285714
\n(d) 0.574128
\nSolution:
\n(b) 0.428571<\/p>\n

Question 7.
\nWhich of the following are not rational numbers?
\n(a) 7\u221a5
\n(b) \\(\\frac{7}{\\sqrt{5}}\\)
\n(c) \\(\\sqrt{36}\\) – 9
\n(d) \u03c0 + 2
\nSolution:
\n(c) \\(\\sqrt{36}\\) – 9<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\nThe product of 2\u221a5 and 6\u221a5 is……….
\n(a) 12\u221a5
\n(b) 60
\n(c) 40
\n(d) 8\u221a5
\nSolution:
\n(b) 60<\/p>\n

Question 9.
\nThe rational number lying between \\(\\frac{1}{5}\\) and \\(\\frac{1}{2}\\)
\n(a) \\(\\frac{7}{20}\\)
\n(b) \\(\\frac{2}{10}\\)
\n(c) \\(\\frac{2}{7}\\)
\n(d) \\(\\frac{3}{10}\\)
\nSolution:
\n(a) \\(\\frac{7}{20}\\)<\/p>\n

Question 10.
\nThe value of 0.03 + 0.03 is ……….
\n(a) 0.\\(\\overline { 09 }\\)
\n(b) 0.\\(\\overline { 0303 }\\)
\n(c) 0.\\(\\overline { 06 }\\)
\n(d) 0
\nSolution:
\n(c) 0.06<\/p>\n

\"Samacheer<\/p>\n

Question 11.
\nThe sum of \\(\\sqrt{343}\\) + \\(\\sqrt{567}\\) is
\n(a) 18\u221a3
\n(b) 16\u221a7
\n(c) 15\u221a3
\n(d) 14\u221a7
\nSolution:
\n(b) 16\u221a7<\/p>\n

Question 12.
\nIf \\(\\sqrt{363}\\) = x\u221a3 then x = ………
\n(a) 8
\n(b) 9
\n(c) 10
\n(d) 11
\nSolution:
\n(d) 11<\/p>\n

Question 13.
\nThe rationalising factor of \\(\\frac{1}{\\sqrt{7}}\\) is ……….
\n(i) 7
\n(b) \u221a7
\n(c) \\(\\frac{1}{7}\\)
\n(d) \\(\\frac{1}{\\sqrt{7}}\\)
\nSolution:
\n(b) \u221a7<\/p>\n

\"Samacheer<\/p>\n

Question 14.
\nThe value of \\((\\frac{1}{3^5})^4\\) is ……..
\n(a) 320<\/sup>
\n(b) 3-20<\/sup>
\n(c) \\(\\frac{1}{3^{-20}}\\)
\n(d) \\(\\frac{1}{3^{9}}\\)
\nSolution:
\n(b) 3-20<\/sup><\/p>\n

Question 15.
\nWhat is 3.976 \u00d7 10-4<\/sup> written in decimal form?
\n(a) 0.003976
\n(b) 0.0003976
\n(c) 39760
\n(d) 0.03976
\nSolution:
\n(b) 0.0003976<\/p>\n

II. Answer the following Questions.<\/p>\n

Question 1.
\nFind any seven rational numbers between \\(\\frac{5}{8}\\) and –\\(\\frac{5}{6}\\)
\nSolution:
\nLet us convert the given rational numbers having the same denominators.
\nL.C.M of 8 and 6 is 24.
\n\"Samacheer
\nNow the rational numbers between
\n\"Samacheer
\nWe can take any seven of them.
\n\"Samacheer<\/p>\n

Question 2.
\nFind any three rational numbers between \\(\\frac{1}{2}\\) and \\(\\frac{1}{5}\\)
\nSolution:
\n\"Samacheer
\nThus the three rational numbers are \\(\\frac{7}{20}\\), \\(\\frac{17}{40}\\) and \\(\\frac{37}{80}\\)<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nRepresent \\(-\\frac{2}{11}\\), \\(-\\frac{5}{11}\\) and \\(-\\frac{9}{11}\\) on the number lines.
\nSolution:
\n\"Samacheer
\nTo Represent \\(-\\frac{2}{11}\\), \\(-\\frac{5}{11}\\) and \\(-\\frac{9}{11}\\) on the number line we make 11 markings each being equal distence \\(\\frac{1}{11}\\) on the left of 0.
\nThe point A represent \\((-\\frac{2}{11})\\), the point B represents \\((-\\frac{5}{11})\\) and the point C represents \\((-\\frac{9}{11})\\)<\/p>\n

Question 4.
\nExpress the following in the form \\(\\frac{p}{q}\\), where p and q are integers and q \u2260 0.
\n(i) 0.\\(\\overline { 47 }\\)
\nSolution:
\nLet x = 0.474747…….. \u2192(1)
\n100 x = 47.4747…….. \u2192(2)
\n(2) – (1) \u21d2 100x – x = 47.4747……..
\n(-) 0.4747<\/span>……..
\n99 x = 47.0000
\nx = \\(\\frac{47}{99}\\)
\n\u2234 0.\\(\\overline { 47 }\\) = \\(\\frac{47}{99}\\)<\/p>\n

(ii) 0.\\(\\overline { 57 }\\)
\nSolution:
\nLet x = 0.57777…….. \u2192(1)
\n10 x = 5.77777…….. \u2192(2)
\n100 x = 57.7777…….. \u2192(3)
\n(3) – (2) \u21d2 100 x – 10 x = 57.7777……..
\n(-) 5.7777<\/span>……..
\n99 x = 52.0000
\nx = \\(\\frac{52}{90}\\) = \\(\\frac{26}{45}\\)
\n\u2234 0.\\(\\overline { 57 }\\) = \\(\\frac{26}{45}\\)<\/p>\n

(iii) 0.\\(\\overline { 245 }\\)
\nSolution:
\nLet x = 0.2454545…….. \u2192(1)
\n10 x = 2.454545…….. \u2192(2)
\n1000 x = 245.4545…….. \u2192(3)
\n(3) – (2) \u21d2 1000 x – 10 x = 245.4545
\n(-) 2.4545<\/span>………
\n990 x = 243.00000
\nx = \\(\\frac{243}{990}\\) (or) \\(\\frac{27}{110}\\)
\n\u2234 0.\\(\\overline { 245 }\\) = \\(\\frac{27}{110}\\)<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nWithout actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
\n(i) \\(\\frac{7}{16}\\)
\n(ii) \\(\\frac{13}{150}\\)
\n(ii) –\\(\\frac{11}{75}\\)
\n(iv) \\(\\frac{17}{200}\\)
\nSolution:
\n(i) \\(\\frac{7}{16}\\) = \\(\\frac{7}{2^4}\\) = \\(\\frac{7}{2^{4} \\times 5^{0}}\\)
\n\u2234 \\(\\frac{7}{16}\\) has a terminating decimal expansion.<\/p>\n

(ii) \\(\\frac{13}{150}=\\frac{13}{2 \\times 3 \\times 5^{2}}\\)
\nSince it is not in the form of \\(\\frac{P}{2^{m} \\times 5^{n}}\\)
\n\u2234 \\(\\frac{13}{150}\\) as non-terminating and recurring decimal expansion.<\/p>\n

(iii) \\(-\\frac{11}{75}=-\\frac{11}{3 \\times 5^{2}}\\)
\nSince it is not in the form of \\(\\frac{P}{2^{m} \\times 5^{n}}\\)
\n\u2234 –\\(\\frac{11}{75}\\) as non-terminating and recurring decimal expansion.<\/p>\n

(iv) \\(\\frac{17}{200}=\\frac{17}{2^{3} \\times 5^{2}}\\)
\n\u2234 \\(\\frac{17}{200}\\) has a terminating decimal expansion.<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\nFind the value of \\(\\sqrt{27}\\) + \\(\\sqrt{75}\\) – \\(\\sqrt{108}\\) + \\(\\sqrt{48}\\)
\nSolution:
\n\"Samacheer
\n= 3\u221a3 + 5\u221a3 – 6\u221a3 + 4\u221a3
\n= 12\u221a3 – 6\u221a3
\n= 6\u221a3
\n= 6 \u00d7 1.732
\n= 10.392<\/p>\n

Question 7.
\nEvaluate \\(\\frac{\\sqrt{2}+1}{\\sqrt{2-1}}\\)
\nSolution:
\n\"Samacheer
\n= 2\u221a2 + 3
\n= 2 \u00d7 1.414 + 3
\n= 2.828 + 3
\n= 5.828<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n= 69984 \u00d7 1021-21-20+9<\/sup>
\n= 69984 \u00d7 10-32<\/sup>
\n= 6.9984 \u00d7 104<\/sup> \u00d7 10-32<\/sup>
\n= 6.9984 \u00d7 10-32+4<\/sup>
\n= 6.9984 \u00d7 10-28<\/sup><\/p>\n

Question 9.
\nWrite
\n(a) 9.87 \u00d7 109<\/sup>
\n(b) 4.134 \u00d7 10-4<\/sup> and
\n(c) 1.432 \u00d7 10-9<\/sup> in decimal form.
\nSolution:
\n(a) 9.87 \u00d7 109<\/sup> = 9870000000
\n(b) 4.134 \u00d7 10-4 <\/sup>= 0.0004134
\n(c) 1.432 \u00d7 10-9<\/sup> = 0.000000001432<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can download Maths Chapter 2 Real Numbers Additional 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 Additional Questions …<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[3],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/268"}],"collection":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/comments?post=268"}],"version-history":[{"count":1,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/268\/revisions"}],"predecessor-version":[{"id":49507,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/268\/revisions\/49507"}],"wp:attachment":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/media?parent=268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/categories?post=268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/tags?post=268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}