Question

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

• A. $2$ or $5$
• B. $2,3$ or $5$
• C. $3$ or $5$
• D. None of these

Answer 1

The correct option is A $2$ or $5$

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

$\left(i\right)\frac{15}{8}=\frac{15}{2\times 2\times 2}=\frac{15}{2^3}=\frac{15\times 5^3}{2^3\times 5^3}=\frac{15\times 125}{8\times 125}=\frac{1875}{1000}=1.875\left(ii\right)\frac{31}{20}=\frac{31}{2\times 2\times 5}=\frac{31\times 5}{2\times 2\times 5\times 5}=\frac{155}{100}=1.55$

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 $5$.