(D) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n \times 5^m$,where $n$ and $m$ are non-negative integers.
Given the fraction $\frac{13}{125}$:
$1$. Prime factorization of the denominator: $125 = 5^3 = 2^0 \times 5^3$.
$2$. Since the denominator is in the form $2^n \times 5^m$ (where $n=0, m=3$),the rational number has a terminating decimal expansion.
$3$. To find the decimal expansion,we make the denominator a power of $10$:
$\frac{13}{125} = \frac{13 \times 2^3}{5^3 \times 2^3} = \frac{13 \times 8}{10^3} = \frac{104}{1000} = 0.104$.