Question
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{129}{2^2\times5^7\times7^{17}}$

Answer

Since the denominator is not of the form $2^m 5^n,$ and it also has $7$ as its factor, the decimal expansion of $\frac{129}{2^2\times5^77^{17}}$ is non-terminating repeating.

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