Question

Assertion (A): \[\frac{22}{7}\] is a nonterminating, repeating decimal.

Reason (R): The rational number \[\frac{p}{q}\] is a terminating decimal, if \[q = (2^{m} \times 5^{n})\] for some whole numbers m and n.

Options

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

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

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

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

Answer 1

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

Explanation:

Step 1 – Assertion: A is true. \[\frac{22}{7}=3.\overline{142857}\] is nonterminating and repeating.

Step 2 – Reason: R is true. It states the denominator condition for a rational number to have a terminating decimal expansion.

Step 3 – Link: The reason gives a criterion for terminating decimals; it does not explain why \[\frac{22}{7}\] is repeating. Thus, R does not correctly explain A.