Question

Show that $\mathrm{0.3333.....}=0.\overline{3}$ can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.

Answer 1

Let, $x=\mathrm{0.3333333...........}=0.\overline{3}$ .....(i)

Multiplying on both sides by '10' we get,

$10x=\mathrm{3.333333...........}=3.\overline{3}$ .........(ii)

Subtract (i) from (ii) we get,

$9x=\mathrm{3.0000000........}=3$

$x=\frac{3}{9}=\frac{1}{3}$

I.e., $\mathrm{0.33333........}=0.\overline{3}=\frac{1}{3}$

Which is in the form of $\frac{p}{q}$. Where $p$ and $q$ are integers.