DECIMAL FRACTIONS - EXERCISE 3 (SOLUTION 71 TO 80)

71.  1/0.0006198 =10000/6.198 = (10000 x 1/6.198) = (10000 x 0.16134) = 16134.

72.  Given, 52416/312 = 168 52416/168 =312.

Now, 52.416/0.0168 = 524160/168 = (52416/168 x 10)= (312 x 10 ) =3120.

73.  Given, 168 x 32 5376 or 5376 / 168 = 32.

Now, 5.376 / 16.8 = 53.76/168 = (5376/168 x 1/100) = 32/100 = 0.32.

74.  Number of decimal places in the given expression = 8.

Number of decimal places in (a) = 8.

Number of decimal places in (b) = 9.

Number of decimal places in (c) = 7.

Clearly, the expression in (a) is the same as the given expression.

75.  For the expressions to be equivalent, the difference between the sum of the decimal places in the numerator and that in the denominator must be equal .This difference is 1 in the given expression and 1 in (d). So, (d).  The answers.

76.  Given expression = (94.54 – 89.63)/(99.54 + 89.63) x (9.654 + 8.963) + 8.963)/(965.4 – 896.3) =  96.54 – 89.63) /(965.4-896.3) x (9.654 +8.963)/(96.54 + 89.63)

= (96.54 – 89.63)/10(96.54 – 89.63) x (96.54 + 89.63)/10 (96.54 + 89.63).

= 1/10 x 1/10 = 1/100 = 1/10² = 10⁻²

77.  (0.11)² + (0.22)³ + …… + (0.99)³ = (0.11)³ (1³ + 2³ + …. + 9³)

=0.001331 x 2025 x 2025 = 2.695275 =2.685. ]

78.  Given expression = 8.7 – [7.6 – {6.5 – (5.4- 2.3)}] = 8.7 –[7.6 – (6.5 – 3.1)]

=8.7- (7.6 – 3.4) = 8.7 – 4.2 = 4.5.

79.  1/4 + 1/4x5 + ¼ x 5 x 6 = 1/4 (1 + 1/5 + 1/30) = 1/4 (30 + 6+1)/30 = 1/4 x 37 /30 = 37/120 = 0.3083.

80.  Given expression= 2 x 4 x 8 x 16 x 4 x 8 x 16 + 8 x 16 + 16 +1 /2 x 4 x 8 x 16

= 1024 +512 +128 + 16 + 1 / 1024 = 1681/1024 = 1.6416.