Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

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Recurring Decimal Number

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Question

Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{15}{1600}$

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\frac{15}{1600},

= \frac{15}{2^{6} \times 5^{2}},

Since prime factorization of the denominator is of the form 2n 5m where m,n are whole numbers

therefore it has terminating decimal.