Question 1

[(0.05) 2 + (0.41) 2 +(0.073) 2] / [(0.005) 2 + (0.041) 2 + (0.0073) 2] =?

Accepted Answer

Given expression = [(0.05)2 + (0.41)2 +(0.073)2] / [(0.005)2 + (0.041)2 + (0.0073)2] Which is in form of [(a2 + b2 + c2)] /[ (a/10)2 + (b/10)2 + (c/10)2] = 100 x (a2 + b2 + c2) / (a2+b2+c2) = 100

Question 2

13.065 x 13.065 - 3.065 x 3.065 =?

Accepted Answer

Given expression =(13.065)2-(3.065)2 =(13.065 + 3.065) x (13.065 - 3.065) =16.13 x 10 = 161.3

Question 3

(.896 x .752 +.896 x .248) / (.7 x .034 + .7 x.966) =?

Accepted Answer

Given expression = (.896 x .752 +.896 x .248) / (.7 x .034 + .7 x.966) =.[896 x (.752+.248)] / [.7 x (.034+.966)] = .(896 x 1) / ( .700 x 1) =896/700 = 1.28

Question 4

(.356 x .365 - 2 x .365 x .106 + .106 x .106) / (.632 x .632 + 2 x .632 x .368 +.368 x .368) =?

Accepted Answer

Given expression = [(.356)2 -2 x .356 x .106 + (.106)2] / [(.632)2+2 x .632 x .368 +(.368)2] = (a2 -2ab + b2) / (c2+2cd+d2) = (a - b)2 / (c + d)2 = (.356 -.106)2 / (.632 + .368)2 = (.25)2 = .0625

Question 5

(3.65 x 3.65 + 2.35 x 2.35 - 2 x 2.35 x 3.65) / 1.69 =?

Accepted Answer

Given expression =[(3.65)2 + (2.35)2 -2 x 3.65 x 2.35 ] / 1.69 =a2 + b2 - 2ab / 1.69, Where a = 3.65 and b = 2.35 =(a - b)2 / 1.69 = (3.65 - 2.35)2 / 1.69 = (1.3)2 / 1.69 = 1.69 / 1.69 = 1

Question 6

( 0.5 x 0.5 x 0.5 x 0.6 x 0.6 x 0.6 ) / ( 0.5 x 0.5 - 0.3 + 0.6 x 0.6 ) =?

Accepted Answer

Given expression = [(0.5)3 + (0.6)3 ] / [(0.5)2 - 0.5 x 0.6 + (0.6)2] = (a3+b3) / ( a2-ab+b2) = a + b = 0.5 + 0.6 = 1.1

Question 7

(.125 + .027) / (.5 x .5 - 1.5 + .09) =?

Accepted Answer

Given expression = [(0.5)3 + (0.3)3] / [(0.5)2 - 0.5 x 0.3 + (0.3)2] = [a3 + b3] / [a2 - ab + b2] = [(a + b)(a2 - ab + b2)] / [a2 -ab + b2] = a+b = 0.5 + 0.3 = 0.8

Question 8

(0.47 x 0.47 x 0.47 - 0.33 x 0.33 x 0.33) / (0.47 x 0.47 + 0.47 x 0.33 + 0.33 x 0.33) =?

Accepted Answer

Given expression = [(0.47)3 - (0.33)3] / [(0.47)2 + 0.47 x 0.33 + (0.33)2] = [a3 - b3 ] / [ a2 + ab + b2] = [(a-b) (a2 + ab + b2)] / [(a2 + ab + b2)] = (a - b) = (0.47 - 0.33) = 0.14

Question 9

(1.04 x 1.04 + 1.04 x 0.04 + 0.04 x 0.04) / (1.04 x 1.04 x 1.04 - 0.04 x 0.04 x 0.04) =?

Accepted Answer

Given Expression = (1.04)2 + 1.04 x 0.04 + (0.04)2 / (1.04)3 - (0.04)3 = (a2 + ab + b2) / (a3 - b3) = (a2 + ab + b2) / [(a-b) (a2 + ab + b2)] = 1 / (a - b) = 1/ (1.04 - 0.04) = 1

Question 10

[(0.87) 3 + (0.13) 3] / [(0.87) 2 - 0.87 x 0.13 + (0.13) 2] =?

Accepted Answer

Given Expression = ( a3 + b3 )/ (a2 + b2 - ab) where = 0.87 and b = 0.13 = [(a + b ) (a2 + b2 - ab)] / (a2 + b2 - ab) = a + b = 0.87 + 0.13 = 1

Question 11

3 / [ 3+ {(0.3 - 3.03) / (3 x 0.91)}] =?

Accepted Answer

Given expression = 3 / [ 3+ {(0.3 - 3.03) / (3 x 0.91)}] = 3 / [3- { 273 / (3 x 91)}] = 3 / (3-1) = 3 / 2 = 1.5

Question 12

[{(0.1) 2 - (0.01) 2} / {0.0001 + 1 }] is equal to?

Accepted Answer

Given expression = (0.01 - 0.0001) / (0.00001 + 1) = (.0099 / .0001) + 1 = 99 + 1 = 100

Question 13

The L.C. M. of 3.0, 0.09 and 2.7 is?

Accepted Answer

The given number are 3.00, 0.09 and 2.70 LCM = LCM of numerator / HCF of denominator L. C. M of 300, 9 and 270 is 2700 ∴ Required L.C.M = 27.00 = 27

Question 14

G. C. D of 1.08, .36 and .9 is?

Accepted Answer

The Given Number are 1.08, .36 and 0.9 G. C. D of 108, 36 and 90 is 18 ∴ Required G. C. D. = 0.18

Question 15

0.1 36 =?

Accepted Answer

= 0.136 = (136 - 1) / 990 = 135 / 990 = 3 / 22

Question 16

0. 63 + 0. 37 =?

Accepted Answer

Given Exp. = 0.63 + 0.37 = 63/99 + 37/99 = 100 / 99 = 11/99 = 1.01

Question 17

(0.34 67 + 0.13 33) =?

Accepted Answer

Given Exp= 0.3467 + 0.1333 = (3467 - 34) / 9900 + (1333 -13) / 9900 = 3433 +1320 / 9900 = 4753 / 9900 = (4801 - 48) / 9900 = 0.4801

Question 18

(3. 57 - 2. 14) =?

Accepted Answer

Given Exp. = 3.57 - 2.14 = 3 + (57 / 99) - 2 - (14 / 99) = 1 + (57 / 99) - (14 /99) = 1 + 43/99 = 1.43

Question 19

( 2. 47 + 3. 53 + 0. 05 ) =?

Accepted Answer

Given Exp. = 247 + 353 + 0.05 = 5 + (47 / 99) + (53 / 99) + (05 / 99) = 5 + (105 / 99) = 5+106/99 =606/99 = 6.06

Question 20

The value of 4. 12 is?

Accepted Answer

4.12 = 4 + 0.12 = 4 + (12 - 1) / 90 = 411/90

Decimal Fraction Questions