Question

Which of the following rational numbers is a terminating decimal?

• A. $\frac{3}{19}$
• B. $\frac{14}{13}$
• C. $\frac{8}{125}$
• D. $\frac{17}{19}$

Answer 1

The correct option is C $\frac{8}{125}$

Consider $\frac{8}{125}$ whose denominator 125 can be expressed in $2^m\times 5^n$ form as $2^6\times 5^3$.
Thus, $\frac{8}{125}$ is a terminating decimal.
However, for rational numbers $\frac{3}{19},\frac{14}{13}$ and $\frac{17}{19}$, their denominators cannot be expressed in the form of $2^m\times 5^n$, where m and n are whole numbers.
Thus, $\frac{3}{19},\frac{14}{13}$ and $\frac{17}{19}$ are non-terminating decimals.
Hence, the correct answer is option (c).