THEORY:
Reduced fraction $\frac{a}{b}$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $b$ (denominator) is of the form $2^n5^m$, where $m$ and $n$ are non-negative integers. For example: $\frac{7}{250}$ is a terminating decimal $0.028$, as $250$ (denominator) equals to $2*5^2$. Fraction $\frac{3}{30}$ is also a terminating decimal, as $\frac{3}{30}=\frac{1}{10}$ and denominator $10=2*5$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $\frac{x}{2^n5^m}$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $\frac{6}{15}$ has 3 as prime in denominator and we need to know if it can be reduced.

BACK TO THE QUESTION:

Only option E (when reduced to its lowest form) has the denominator of the form $2^n5^m$: 39/128=39/2^7.

Answer: E.