Question

Choose the following:
Convert the decimal $0.666666\dots$ into a fraction

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

Answer 1

The correct option is D $\frac{2}{3}$

Let, $F=0.666666\dots \left(i\right)$
On multiplying both the sides by $10,$ we get,
$\Rightarrow 10F=6.666666\dots \left(ii\right)$
On substracting equation $\left(i\right)$ from $\left(ii\right),$ we get
$\Rightarrow 9F=6$
$\Rightarrow F=\frac{6}{9}\Rightarrow F=\frac{2}{3}$