A rational number can be expressed as a terminating decimal if the denominator has factors:

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Rational Numbers

Question

A rational number can be expressed as a terminating decimal if the denominator has factors:

3 or 5

2,3 or 5

None of these

2 or 5

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Any rational number with its denominator is in the form of 2^m×5ⁿ, where m,n are positive integers and are terminating decimals. The examples are shown below:

\frac{15}{8} = \frac{15}{2 \times 2 \times 2} = \frac{15}{2^{3}} = \frac{15 \times 5^{3}}{2^{3} \times 5^{3}} = \frac{15 \times 125}{8 \times 125} = \frac{1875}{1000} = 1.875

$(ii) \frac{31}{20} = \frac{31}{2 \times 2 \times 5} = \frac{31 \times 5}{2 \times 2 \times 5 \times 5} = \frac{155}{100} = 1.55$

In both the examples, the result is a terminating decimal because terminating decimal is a decimal which can be expressed in a finite number of figures.

Hence, a rational number can be expressed as a terminating decimal if the denominator has factors 2 or 5.