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

Foundation

Mathematics Foundation

Recurring Decimal Number

Properties of Real Number

Linear Equations in One Variable

Question

Without actually performing the long division,state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion: $\frac{13}{3125}$

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A simplified fraction of the form $\frac{p}{q}$ has a terminating decimal expansion if and only if all the prime factors of q are either 2 or 5.
Given: $q = 3125 = 5 5$
As the only prime factor of the denominator is 5, the decimal expansion will be terminating.