Question

$0.\overline{67}$ can be represented as.

• A. $\frac{67}{99}$
• B. $\frac{67}{89}$
• C. $\frac{67}{79}$
• D. None of the above

Answer 1

The correct option is A $\frac{67}{99}$

$Z=0.\overline{67}$
$\begin{array}{c}100Z=\mathrm{67.6767...}1)\\ Z=\mathrm{0.6767...}2)\\ -------\\ 99Z=67.000\end{array}$

$($ On subtracting equation $1)$ from $2)$ $)$
$Z=\frac{67}{99}$