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Question

# Assertion (A): 299261 will have a non-terminating, non-repeating decimal expansion. Reason (R): Let a=pq be a rational number such that p and q are co-prime and the prime factorisation of q is of the form 2n×5m, 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)
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B
(A) is false and (R) is the correct explanation of (A)
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C
(A) is true and (R) is false
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D
Both (A) and (R) are false
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Solution

## The correct option is C (A) is true and (R) is falseGiven number=299261 =293×3×3×7×7×7=2933×73 9261=33×73 is not of the form 2n×5m. Hence, Assertion is true but the Reason is false because if the denominator of the rational number can be expressed in the form 2n×5m, where n and m are non-negative integers, then rational number has a decimal expansion, which is terminating.

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