Question

Find the $\frac{p}{q}$ form of $\mathrm{0.666...}$ is
Where $p,q\in Z$ and $q\ne 0$.

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

Answer 1

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

Let $x=\mathrm{0.666...}$------------ $\left(1\right)$

Multiply by $10$ both sides we get,
$10x=\mathrm{6.666...}$------------ $\left(2\right)$

Subtracting the two equations
$10x-x=\mathrm{6.666...}-\mathrm{0.666...}$
$9x=6$
Dividing by $9$ on both the sides we get,
$\frac{9x}{9}=\frac{6}{9}$

$x=\frac{2\times 3}{3\times 3}$-----$\left(3\right)$

$x=\frac{2}{3}$

Answer: Hence $\frac{p}{q}$ form of $\mathrm{0.666...}$ is $\frac{2}{3}$