Question

Express 1.4191919..... in the form of $\frac{p}{q}$ , where p and q are integer and q $\ne$ 0.

Answer 1

Given, the expression $\mathrm{1.4191919...}$

Let $\mathrm{1.4191919....}=x$ $⟹\left(i\right)$.

Multiplying $\left(i\right)$ by $10$,

$⟹\mathrm{14.191919....}=10x$ $⟹\left(ii\right)$.

Multiplying $\left(ii\right)$ by $1000$,

$⟹\mathrm{1419.191919....}=1000x$$⟹\left(iii\right)$.

Then, $\left(iii\right)-\left(ii\right)$

$⟹$ $1000x-10x=\mathrm{1419.191919....}-\mathrm{14.191919....}$

$⟹$ $990x=1405$

$⟹x=\frac{1405}{990}=\frac{281}{198}$.

Hencs, $\mathrm{1.4191919...}$ in $\frac{p}{q}$ is $\frac{281}{198}$.