Question

Assertion: `7/120` is terminating repeating decimal expansion.

Reason: π is an irrational number.

विकल्प

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

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

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

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

Answer 1

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

Explanation:

The fraction `7/120` is a rational number.

To determine if its decimal expansion is terminating or repeating, we look at the denominator’s prime factors after simplification.

120 = 2³ × 3 × 5. Since the denominator has a factor of 3 in addition to 2s and 5s, the decimal expansion of `7/120` is non-terminating repeating, not terminating.

Therefore, the Assertion that `7/120` has a terminating repeating decimal expansion is false.

The Reason states that π is an irrational number, which is true.

However, the Reason is not related to the decimal nature of `7/120`, so it is not an explanation for the Assertion.

Thus, the assertion is false, but the reason is true.