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 $\frac{ p }{ q }$ is q which is not in the form of $\left(2^m \times 5^n\right)$, where m , n are nonnegativ inteagrs.
The condition for non-terminating decimal expansion is that denominator of $\frac{ p }{ q }$ is q which is not in the form of $\left(2^m \times 5^n\right)$, where m , n are nonnegativ inteagrs.
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