Is there a way to determine that for some number $\displaystyle a$ in base m that it will or will not have a terminating equivalent number $\displaystyle b$ in base n?

For example, when converting number 0.315 in base 10 to base 2, we get the base 2 number 0.01010000101000111101011100001010... I assume this will be nonterminating. How can I actually prove that this number will be nonterminating?

Thanks