Question

Write the recurring decimal $0.6\overline{3}$ as a fraction in its lowest terms.

Answer 1

Let $x=0.6333⟶\left(i\right)$

$10x=6.3333⟶\left(ii\right)$

$\left(ii\right)-\left(i\right),$ we have $,$

$\Rightarrow 9x=5.7$

$\Rightarrow x=\frac{5.7}{9}$

$=\frac{57}{90}$

$=\frac{19}{30}$ $.$