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Math Topic - Decimal Fraction

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Published in: Mathematics
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Helpful Notes for students who are preparing for competitive exams.

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  1. PBI PBI INSTITUTE Decimal Fraction: Fractions in which denominators are powers of 10 are known as decimal fractions. Eg. 1/10 = 0.1, 1/100 = 0.01 , 5/1000 = 0.005 Recurring Decimal: If in a decimal fraction a figure is repeated continuously then such a number is called recurring decimal. It is expressed by putting a bar on the set. Eg. 1/3 = 0.3333, 22/7 = 3.142857 142857 Pure Recurring Decimal: A decimal fraction in which all the figures after the decimal point are repeated. Eg. 0.555555 = 5/9, 0.535353 = 53/99 Mixed Recurring Decimal: A decimal fraction in which some figures do not repeat and some are repeated. Eg. 0.17333 1. What decimal of an hour is a second? A. .0025 c. .00027 B. .0256 .000126 D. Solution Required decimal = 1/ 60 x 60 = 1/ 3600 = .00027. 2. The value of + is A. 0.47 C. 470 Solution Given expression B. 47 D. 4700 = 4.7 x100 = 470. 3. The value of (0.2x0.2+0.01) (0. Ix0.1+0.02)-1 is equal to
  2. PBI IN A. 5/3 C. 41/4 Solution Given expression PBI INSTITUTE B. 9/5 D. 41/12 = 0.04+0.01/0.01+0.02 = 0.05 / 0.03 4. Which one of the following is equal to 3.14x106? A. 314 c. 3140000 Solution Given, 3.14 x 106 5. A. 0.000196 c. 19.6 Solution Sum of decimals places= 6. = 3140000. = 196. = 0.000196 B. 3140 D. None of these B. 0.00196 D. 196 6. A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can be make out of this cloth? A. 300 B. 360
  3. PBI c. 400 Solution Length of each pieces PBI INSTITUTE = 0.125 m Required number of pieces(37.5/0.125) D. None of these = / 125) = 300. 7. The expression (11.98xl 1.98+11.98xx +0.02x0.02) will be a perfect square for x equal to A. 0.02 c. 0.04 Solution Given expression For the given expression to be a perfect square, we must have 11.98x X 8. 12.1212+17.0005 - 9.1102 = ? A. 20.0015 c. 20.0115 B. 0.2 D. 0.4 = 0.04 B. 20.0105 D. 20.1015 Solution Given expression 9. = (29.1217 - 9.1102) =20.0115. 4.036 divided by 0.04 gives A. 1.009 c. 10.9 Solution 4.036 / 0.04 10. = 403.6 / 4 = 100.9 If 2994 — •145 . . = 172, then 29.94+ 1.45 A. 172 c. 1.72 = 299.4/14.5 B. 100.09 D. None of these B. 0.172 D. 17.2 Solution (29.94/1.45) = 172/10 = 17.2. 11. The value of - 0.098)2 / is B. 0.235 A. 0.039 c. 0.25 SD. 4
  4. PBI Solution Given expression 12. A. 30 c. 80 Solution Given expression= PBI INSTITUTE = (a+b)2 - (a-b)2/ab = 4ab/ab is equal to = (a2+2ab+b2) = (a-I-b)2 = (7.5+2.5)2 = 102 = 100. B. 60 D. 100 13. The value of 3.6x0.48x2.50 / 0.12x0.09x0.5 is A. 80 c. 8000 Solution Therefore 14. Given that 268x74= A. 1.9832 c. 1.5693 Solution Sum of decimals places Therefore, B. 800 D. 80000 =3.6xo.48x2.50/o.12xo.09xo.5 = 36x48x250/12x9x5 = 800. 19832, find the value of 2.68x.74. B. 1.0025 D. 1.0266 = 1.9832.

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