| Assertion (A): The rational number \[\frac{117}{819}\]has a terminating decimal expansion. |
| Reason (R): Let \[x=p/q\] be a rational number, such that the crime factorisation of q is not of the form \[{{2}^{n}}\times {{5}^{m}},\]decimal expansion, which is non-terminating repeating (recurring). |
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: D
Solution :
| Sol. [d] We have, \[\frac{p}{q}=\frac{117}{819}=\frac{3\times 3\times 13}{3\times 3\times 7\times 13}=\frac{1}{7}\] |
| Here, the denominator q has only prime factor 7, so, \[p/q\] has a non-terminating repeating decimal expansion. |
| \[\therefore \] Assertion: False; Reason: True. |
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