Decimal Fractions with Explanation

Q1. The simplification of gives:

Answer- Option A

Explanation-

0.2 x 0.2 + 0.02 x 0.02 - 0.4 x 0.02 = 0.2 x 0.2 + 0.02 x 0.02 - 2 x 0.2 x 0.02
= (a² + b² - 2ab) = (a - b)²
= (0.2 - 0.02)²
= (0.18)².
Given expression =

(0.18 x 0.18) 0.36

= 0.09.

Q2. The value of is:

Answer- Option C

Explanation-

Given expression =

(2.3)3 - (0.3)3 (2.3)2 + (2.3 x 0.3) + (0.3)2

=

a3 - b3 a2 + ab + b2

= (a - b) = (2.3 - 0.3) = 2.

Q3. is equal to:

Answer- Option B

Explanation-

Given expression =

[(0.6)2 - (0.5)2]2 (0.6)2 + (0.5)2

=

[(0.6)2 + (0.5)2] [(0.6)2 - (0.5)2] (0.6)2 + (0.5)2

= (0.6)² - (0.5)² = (0.6 + 0.5)(0.6 - 0.5)
= 0.11.

Q4. If 213 x 16 = 3408, then 1.6 x 21.3 is equal to:

Answer- Option C

Explanation-

1.6 x 21.3 =

16 10

x

213 10

=

3408 100

= 34.08.

Q5. The value of 0.0396 ÷ 2.51 correct to 2 significant figures is:

Answer- Option D

Explanation-

0.0396 2.51

=

3.96 251

=

396 251 x 100

=

1.577 100

= 0.016.

Q6. A tailor has 37.5 meters of cloth, and he has to make 8 pieces out of a meter of cloth. How many pieces can be make out of this cloth?

Answer- Option B

Explanation-

Length of each piece = 0.125 m.
Required number of pieces =

37.5 0.125

=

375 x 100 125

= 300.

Q7. The least among the following is:

Answer- Option D

Explanation-

1 ÷ 0.2 =

10 2

= 5; 0.2‾ = 0.222.......; (0.2)² = 0.04.
0.04 < 0.2 < 0.22 ....... < 5.