Question

Which of the following fraction(s) is/are non terminating?

• A. $\frac{1}{2}$
• B. $\frac{1}{5}$
• C. $\frac{1}{6}$
• D. $\frac{1}{3}$

Answer 1

Answer: (C), (D)

The correct options are
C $\frac{1}{6}$
D $\frac{1}{3}$

For terminating decimals, the denominator is of the form $2^n$, $5^m$ or $2^n\times 5^m$.

$\frac{1}{2}=0.5$
It can be seen the denominator is of the form $2^n$, with n = 1 in this case.
Hence, it is terminating.

$\frac{1}{5}=0.2$
It can be seen the denominator is of the form $5^m$, with m = 1 in this case.
Hence, it is terminating.

$\frac{1}{6}=\mathrm{0.166666666..}$
It can be seen the denominator is not of the form $2^n$, $5^m$ or $2^n\times 5^m$.
Hence, it is non terminating.


$\frac{1}{3}=\mathrm{0.333333333333..}$
It can be seen the denominator is not of the form $2^n$, $5^m$ or $2^n\times 5^m$.
Hence, it is non terminating.