Question

Which of the following has a non terminating decimal expansion?

• A. $\frac{17}{210}$
• B. $\frac{23}{8}$
• C. $\frac{17}{80}$
• D. $\frac{35}{50}$

Answer 1

The correct option is A

$\frac{17}{210}$

A rational number in the form of $\frac{p}{q}$ is a terminating decimal if q can be expressed as $2^m\times 5^n$ where m and n are non negative positive integers.

$\frac{17}{210}$,
Here, q = 210 = $2\times 3\times 5\times 7$
since denominator is not in the form of $2^m\times 5^n$, the rational number has non terminating decimal expansion.

$\frac{23}{8}$
Here, 8 = $2^3\times 5^0$
$\therefore$ The rational number has terminating decimal expansion.

$\frac{17}{80}$
Here, 80= $2^4\times 5^1$
The rational number has terminating decimal expansion.

$\frac{35}{50}$
50 = $2\times 5\times 5$

The rational number has terminating decimal expansion.Hence the option 1 is a non-terminating decimal expansion.