Prove that when the denominator of a rational number is of the form $2^n * 5^m$ it is a terminating decimal

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What is the proof for when the denominator of a rational number is of the form $2^n * 5^m$ it is a terminating decimal?

For example: $7/8$, where $8$ is of the form $2^3 * 5^0$ Therefore, $7/8$ is a terminating decimal

But why does this work?

What is the proof?