State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{13}{3125}$

(A) To determine if the rational number $\frac{13}{3125}$ has a terminating decimal expansion,we examine the prime factorization of the denominator.
Step $1$: Find the prime factorization of $3125$.
$3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^5$.
Step $2$: $A$ rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of $q$ is of the form $2^n \times 5^m$,where $n$ and $m$ are non-negative integers.
Here,$q = 5^5 = 2^0 \times 5^5$. Since the denominator is in the form $2^n \times 5^m$,the rational number has a terminating decimal expansion.
Step $3$: To find the decimal expansion,multiply the numerator and denominator by $2^5$ to make the denominator a power of $10$.
$\frac{13}{3125} = \frac{13 \times 2^5}{5^5 \times 2^5} = \frac{13 \times 32}{10^5} = \frac{416}{100000} = 0.00416$.