Question

If the rational number $\frac{a}{b}$ has a terminating decimal expansion, what is the condition to be satisfied by $b$?

Answer 1

The rational number $\frac{a}{b}$ has a terminating decimal expansion, if the prime factorization of $b$ is of the form $2^m\times 5^n$ only; where $n,m$ are non-negative integers.

Example: $\frac{7}{80}=\frac{7}{2^4\times 5^1}$

$\frac{7}{80}$ is a rational number as the prime factorisation of denominator is $2^m\times 5^n$, where $n$ and $m$ are non-negative integers.