Question

How do you convert $0.4$ ($4$ being repeated) to a fraction?

Answer 1

Solve for the required fraction:

Given that $0.4$ ($4$ being repeated)

Let $\mathrm{x}=0.444...$

$\Rightarrow$ $\mathrm{x}=0.\overline{4}$ $...\left(\mathrm{i}\right)$

$\Rightarrow$$10\mathrm{x}=4.\overline{4}$ $...\left(\mathrm{ii}\right)$

Subtract $\left(\mathrm{i}\right)$ from $\left(\mathrm{ii}\right)$, we get;

$10\mathrm{x}-\mathrm{x}=4.\overline{4}-0.\overline{4}$

$\Rightarrow$ $9\mathrm{x}=4$

$\Rightarrow$ $\mathrm{x}=\frac{4}{9}$

Hence, $0.4$ ($4$ being repeated) in fraction is $\frac{4}{9}$.