Decimal Fractions — Assertion-Reason Questions

Assertion. The place value of the digit 4 in 2.147 is $\dfrac{4}{100}$

Reason. The place value of a digit at hundredths place is 10 times the same digit at the tenths place.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

In the number 2.147, the digit 4 is in the hundredths place. So, its place value is $\dfrac{4}{100}$.

So the Assertion (A) is true.

The place value of a digit at the hundredths place is actually $\dfrac{1}{10}$ of the value it would have at the tenths place, not 10 times.

So the Reason (R) is false.

Option 3 is the correct option.

Assertion. The decimal numbers 2.5, 2.05, 2.005 and 2.0005 are equivalent.

Reason. Any number of zeros put at the end of a decimal number does not change its value.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

The decimal numbers 2.5, 2.05, 2.005 and 2.0005 are not equivalent because the zero is being placed between the decimal point and the digit $5$ which changes its place value from tenths to hundredths, and so on.

Therefore the Assertion (A) is false.

Adding zeros at the end of a decimal number does not change its value. For example, 2.5 = 2.50, the value does not change.

So the Reason (R) is true.

Option 4 is the correct option.