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

Properties of Real Number

Recurring Decimal 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: $\frac{35}{50}$

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Let,

\frac{35}{50} = \frac{7}{10}

Cheking co-prime

7 and 10 have no common factor

Therefore,

7 and 10 are co-prime.

For denominator = 10 = 2¹ ×5¹

Therefore,

denominator is of the form 2ⁿ5^m

Where

m = 1.n = 1

Hence the

\frac{7}{10}

and

\frac{35}{50}

are the terminating decimal.