| Assertion (A): Denominator of\[\text{34}.\text{12545}\]. When expressed in the form \[\frac{p}{q},\]\[q\ne 0,\] is of the form \[{{2}^{m}}\times {{5}^{n}},\]where m, n are non-negative integers. |
| Reason (R): \[\text{34}.\text{12545}\] is a terminating decimal fraction. |
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] Reason is clearly true Again \[\text{34}.\text{12545=}\frac{3412345}{100000}=\frac{682469}{20000}=\frac{682469}{{{2}^{5}}\times {{5}^{4}}}\] |
| Its denominator is of the form \[{{2}^{m}}\times {{5}^{n}}\] |
| [\[m=5,\]\[n=4\] are non-negative integers) |
| Hence, assertion is true. Since reason gives assertion holds. |
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