Which of the following numbers has terminating decimal expansion?

\frac{37}{45}

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\frac{21}{2^{3} 5^{6}}

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\frac{17}{49}

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\frac{89}{2^{2} 3^{2}}

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Solution

The correct option is D $\frac{21}{2^{3} 5^{6}}$
If numerator and denominator are co-prime then fraction will terminate only if denominator will be of type $2^{m} 5^{n}$ .
Only option B satisfies this criteria so correct answer will be option B

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Similar questions

Q. Which of the following numbers has terminating decimal expansion?

(a)

\frac{37}{45}

(b)

\frac{21}{2^{3} 5^{6}}

(c)

\frac{17}{49}

(d)

\frac{89}{2^{2} 3^{2}}

Q. Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.

\frac{17}{8}

Q. Which of the following rational numbers has non terminating and repeating decimal expansion?

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{17}{8}$

Q. Without actual division find whether

\frac{17}{68}

has terminating of non-terminating recurring decimal expansion?

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Which of the following numbers has terminating decimal expansion?

The correct option is D 212356If numerator and denominator are co-prime then fraction will terminate only if denominator will be of type 2m5n .Only option B satisfies this criteria so correct answer will be option B

The correct option is D $\frac{21}{2^{3} 5^{6}}$
If numerator and denominator are co-prime then fraction will terminate only if denominator will be of type $2^{m} 5^{n}$ .
Only option B satisfies this criteria so correct answer will be option B