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Question

# Assertion (A) $\frac{1242}{49}$is a non-terminating, repeating decimal. Reason (R) The rational number $\frac{p}{q}$ is a terminating decimal if q = (2m × 5n) for some whole numbers m and n. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

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Solution

## (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). $\frac{1242}{49}=\frac{1242}{{7}^{2}}$ = a non-terminating, repeating decimal We know 7 is not a factor of 1242; so, it is in its simplest form. Moreover, it is not of the form $\left({2}^{m}×{5}^{n}\right)$.

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