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:

Foundation

Mathematics Foundation

Recurring Decimal Number

Properties of Real Number

Linear Equations in One Variable

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: $\frac{13}{3125}$

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Let us consider factor of denominator 3125 = 5 × 5 × 5 × 5 × 5 = 5⁵

Denominator

= 5⁵= 2⁰× 5⁵= 2⁰× 5⁵

in the form

2 n 5 m

Where m = 0,n = 5

Thus they are terminating decimal.