Check if $\frac{131}{2^{3} \times 5^{4}}$ have terminating or non-terminating decimal expansion

If yes then answer $1$ , if no the answer $0$

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Solution

$\frac{131}{2^{3} \times 5^{4}}$ has terminating decimal expansion.

Expressing the denominator in the form of prime factorization in $2$ and $5$ .

$2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5$

We know that denominators that are expressed only in $2$ and $5$ have terminating decimal expansion.

Since the denominator does have it so it has terminating decimal expansion

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Check if 13123×54 have terminating or non-terminating decimal expansionIf yes then answer 1, if no the answer 0

Check if $\frac{131}{2^{3} \times 5^{4}}$ have terminating or non-terminating decimal expansion

If yes then answer $1$ , if no the answer $0$