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{6}{15}

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Rational Numbers

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{6}{15}

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Let,

\frac{6}{15} = \frac{2}{5}

Checking co-prime

2

and

5

are no factor

Therefore

2

and

5

are co prime

For denominator

= 5 = 2^{0} \times 5^{1}

in the form of

2^{n} 5^{m}

where

m = 1, n = 0

Hence they are terminating decimal