Question

Assertion (A): $\frac{29}{9261}$ will have a non-terminating, non-repeating decimal expansion.
Reason (R): Let $a=\frac{p}{q}$ be a rational number such that $p$ and $q$ are co-prime and the prime factorisation of $q$ is of the form $2^n\times 5^m$, where $n$ and $m$ are non-negative integers. Then $a$ has a decimal expansion, which is non-terminating.

• A. (A) and (R) are true and (R) is the correct explanation of (A)
• B. (A) is false and (R) is the correct explanation of (A)
• C. (A) is true and (R) is false
• D. Both (A) and (R) are false

Answer 1

The correct option is C (A) is true and (R) is false

Given number$=\frac{29}{9261}$
$=\frac{29}{3\times 3\times 3\times 7\times 7\times 7}=\frac{29}{3^3\times 7^3}$
$9261=3^3\times 7^3$ is not of the form $2^n\times 5^m$.
Hence, Assertion is true but the Reason is false because if the denominator of the rational number can be expressed in the form $2^n\times 5^m$, where $n$ and $m$ are non-negative integers, then rational number has a decimal expansion, which is terminating.