| Assertion (A): \[\frac{1242}{49}\]is a non-terminating repeating decimal. |
| Reason (R): The rational number \[\frac{p}{q}\] is a terminating decimal, if \[q=({{2}^{m}}\times {{5}^{n}})\]for some whole numbers m and n. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)
C) Assertion (A) is true but reason (R) is false
D) Assertion (A) is false but reason (R) is true
Correct Answer: A
Solution :
| Sol. [a] \[\frac{1242}{49}=\frac{1242}{{{7}^{2}}}\] Denominator has one factor namely 7, which is other than 2 and 5. |
| So, given rational number is a non-terminating repeating decimal. |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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