Question

What is the decimal form of $(0.\overline{3}{)}^2$.

Answer 1

Decimal form of $(\mathrm{0.33333....}{)}^2$

Let $x=0.3333$…..

$x=0.\overline{3}$ …………$\left(1\right)$

Multiply the above equation by $10$

$10x=3.\overline{3}$ ……………$\left(2\right)$

Now subtract $\left(1\right)$ from $\left(2\right)$

$10x-x=3.\overline{3}-0.\overline{3}$

$9x=3$

$x=\frac{3}{9}$

$x=\frac{1}{3}$

$\Rightarrow x=0.\overline{3}=\frac{1}{3}$

$x^2=(0.\overline{3}{)}^2={\left(\frac{1}{3}\right)}^2$

$(\mathrm{0.33.....}{)}^2=\frac{1}{9}$.