Question

Assertion (A): \[0.\overline{6}\] is a terminating 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

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

Explanation:

Step 1 – Assertion: A is false. Let \[x=0.\overline{6}\]. Then \[10x=6.\overline{6}\], so \[9x=6\] and \[x=\frac{2}{3}\]. Its denominator has a factor other than 2 or 5, so the decimal is nonterminating and repeating.

Step 2 – Reason: R is true. A rational number whose denominator has only 2 and 5 as prime factors has a terminating decimal expansion.