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A rational number $\frac{p}{q}$ (in lowest terms) has a terminating decimal expansion only when $q$ can be written in the form:

Class 10Decimal ExpansionsNumber Systems

A $2^{n} \times 5^{m}$
B $2^{n} \times 3^{m}$
C $3^{n} \times 5^{m}$
Dany prime power

Step-by-Step Solution

A rational number

\frac{p}{q}

in lowest terms terminates exactly when the denominator

q

has only 2 and 5 as prime factors, i.e.

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

.

Answer: A)

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

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