Question

Which of the following options represents terminating decimals?

• A. $\frac{2}{9}$
• B. $\frac{1}{11}$
• C. $\frac{15}{4}$
• D. $\frac{1}{6}$

Answer 1

The correct option is C $\frac{15}{4}$

A terminating decimal is a decimal number that has a finite number of decimals.

A fraction is a terminating decimal if the prime factors of the denominator in its lowest form contain only $2s$ or $5s$ or both 2s and 5s or no prime factors at all.

In fraction $\frac{2}{9},9$ is the denominator which don't have prime factors 2 or 5, so $\frac{2}{9}$ is not a terminating decimal

In fraction $\frac{1}{11},11$ is the denominator whose prime factors are neither 2 nor 5 , so $\frac{1}{11}$ is not a terminating decimal

In fraction $\frac{1}{6},6$ is the denominator whose prime factors are 2 and 3 but for a fraction to be a terminating decimal, it's denominator should have Only 2s or 5s or both as prime factors So, $\frac{1}{6}$ is not a terminating decimal

$\text{In fraction}\frac{15}{4},4$ is the denominator whose prime factors are only 2s
$\Rightarrow \frac{15}{4}=\frac{15}{2\times 2}\text{= 3.75}\text{So,}\frac{15}{4}\text{is a terminating decimal}$