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The condition to be satisfied by q so that a rational number $\frac{p}{q}$ has a terminating decimal expansion is [[1]].

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answer is 2 M × 5 N.

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Detailed Solution

The condition to be satisfied by q so that a rational number

\frac{p}{q}

has a terminating decimal expansion is

2^{m} \times 5^{n}

.
We know that rational numbers are the numbers which are represented in the form of

\frac{p}{q}

where q is not equal to zero. It is a real number.
Assume the number be of the form

\frac{p}{q}

where both p and q are co-prime rational numbers.
For the number to have a terminating decimal expansion, q must be of the form

2^{m} \times 5^{n} .

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The condition to be satisfied by q so that a rational number pq has a terminating decimal expansion is [[1]].