$A$ rational number in its decimal expansion is $327.7081$. What can you say about the prime factors of $q$,when this number is expressed in the form $\frac{p}{q}$? Give reasons.

(A) The given number $327.7081$ is a terminating decimal number.
Since it is a terminating decimal,it represents a rational number whose denominator $q$,when expressed in the form $\frac{p}{q}$ (where $p$ and $q$ are coprime),must have prime factors of the form $2^{m} \times 5^{n}$,where $m$ and $n$ are non-negative integers.
We can write:
$327.7081 = \frac{3277081}{10000} = \frac{p}{q}$
Here,the denominator $q = 10000 = 10^{4}$.
Expanding the prime factors of $q$:
$q = (2 \times 5)^{4} = 2^{4} \times 5^{4}$.
Thus,the prime factors of $q$ are only $2$ and $5$.