Decimal Fractions — Assertion Reason Type Questions

Assertion (A): 48.36 ÷ 10 = 4.836, 48.36 ÷ 100 = 0.4836, 48.36 ÷ 1000 = 0.04836, etc.

Reason (R): 48.36 ÷ 10 = $\dfrac{48.36}{10} = \dfrac{4836}{100 \times 10} = \dfrac{4836}{1000}$ = 4.836 and

48.36 ÷ 100 = $\dfrac{48.36}{100} = \dfrac{4836}{100 \times 100}$ = 0.4836 and so on.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

On dividing 48.36 by 10, 100 and 1000, the decimal point shifts to the left by 1, 2 and 3 places respectively, giving 4.836, 0.4836 and 0.04836.

So, Assertion (A) is true.

Now, 48.36 ÷ 10 = $\dfrac{48.36}{10} = \dfrac{4836}{100 \times 10} = \dfrac{4836}{1000}$ = 4.836

and

48.36 ÷ 100 = $\dfrac{48.36}{100} = \dfrac{4836}{100 \times 100}$ = 0.4836.

So, Reason (R) is also correct.

Hence, option 3 is the correct option.

Assertion (A): 0.094 × 10 = 0.94, 0.094 × 100 = 9.40, 0.094 × 1000 = 94, etc.

Reason (R): When multiplying a decimal number by 10, 100, 1000, etc., the decimal point is shifted one place, two places, three places respectively to the right-side of the decimal point.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

0.094 × 10 = 0.94, 0.094 × 100 = 9.40 and 0.094 × 1000 = 94, so Assertion (A) is true.

The Reason (R) correctly states the rule of shifting the decimal point to the right and is also true.

Hence, option 3 is the correct option.