Question

The rational number which can be expressed as a terminating decimal is:

• A. $\frac{1}{6}$
• B. $\frac{1}{12}$
• C. $\frac{1}{15}$
• D. $\frac{1}{20}$

Answer 1

Answer: (D)

$\frac{1}{20}$

A terminating decimal is a decimal that ends after a finite number of steps. It's a decimal with a finite number of digits.

Also, a decimal is terminating if in fully reducible form, the denominator is composed of $2$'s and $5$'s only.

Here, only option $D$ has a denominator composed of $2$'s and $5$'s, i.e. $20=2^2\times 5$

and $\frac{1}{20}=0.05$.

In all the other options, the decimal does not end with a finite number of digits and the denominator has factors other than $2$'s and $5$'s.

Therefore, option $D$ is correct.