If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as:
(Here, n and m are non-negative integers.)

$3^{n} 5^{m}$

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$\frac{2^{n}}{5^{m}}$

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$\frac{7^{n}}{5^{m}}$

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$2^{n} 5^{m}$

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Solution

The correct option is D
$2^{n} 5^{m}$

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then the prime factorisation of $q$ will be in the form of $2^{n} 5^{m}$ .

Example:
Consider rational number $\frac{1}{8}$ .
Here, denominator $8 = 2^{3} \times 5^{0}$
Therefore, the rational number $\frac{1}{8}$ will have terminating decimal expansion.
$\frac{1}{8} = 0.125$ which is terminating.
Hence verified.

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If pq is a rational number with terminating decimal expansion where p and q are coprimes, then q can be represented as: (Here, n and m are non-negative integers.)

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as:
(Here, n and m are non-negative integers.)