Write the condition to be satisfied by q so that a rational numbe… - Vidyadip

Question

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

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Answer

Let rational number be $n$ which is in the form of $\frac{\text{p}}{\text{q}}.$
The condition for non-terminating decimal expansion is that denominator of $\frac{\text{p}}{\text{q}}$ is $q$ which is not in the form of $(2^m× 5^n)$, where $m, n$ are non-negativ inteagrs.

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