# Write the condition to be satisfied by q so that a rational number

Question:

Write the condition to be satisfied by $q$ so that a rational number $\frac{p}{q}$ has a terminating decimal expansions.

Solution:

We need to find the condition to be satisfied by $q$ so that a rational number $\frac{p}{q}$ has a terminating decimal expression.

For the terminating decimal expression, we should have a multiple of 10 in the denominator.

Hence, the prime factorization of $q$ must be of the form $2^{m} \times 5^{n}$, where $m$ and $n$ are non-negative integers.