Without actually performing the long division, state whether the following rational numbers 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.

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Linear Equations in One Variable

Question

Without actually performing the long division, state whether the following rational numbers 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. $\frac{23}{2^{3} 5^{2}}$

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clearly ,the prime factorisation of the denominator of $\frac{23}{2^{3} \times 5^{2}}$ is of the form 2^m × 5ⁿ. so it has terminating decimal expansion which terminates after max (3,2) = 3
places of decimals.