State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{64}{455}$

(N/A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$.
If $q = 2^n \times 5^m$,where $n$ and $m$ are non-negative integers,the decimal expansion is terminating.
Here,the fraction is $\frac{64}{455}$.
First,we check if the fraction is in its simplest form. The $g.c.d.$ of $64$ and $455$ is $1$,so it is in its simplest form.
Next,we find the prime factorization of the denominator $455$:
$455 = 5 \times 91 = 5 \times 7 \times 13$.
Since the prime factorization of the denominator contains factors other than $2$ and $5$ (specifically $7$ and $13$),the rational number $\frac{64}{455}$ does not have a terminating decimal expansion. It has a non-terminating repeating decimal expansion.