Question

Express $0.\overline{2}$ as a fraction in its lowest form.

• A. $\frac{2}{9}$
• B. $\frac{4}{9}$
• C. $\frac{1}{9}$
• D. $\frac{5}{9}$

Answer 1

The correct option is A

$\frac{2}{9}$

$0.\overline{2}=\mathrm{0.222222.....}$

$=0.2+0.02+0.002+\cdots \cdots$

$=\frac{2}{10}+\frac{2}{100}+\frac{2}{1000}+\cdots \cdots$

$=\frac{\frac{2}{10}}{1-\frac{1}{10}}$ $(a=\frac{2}{10},r=\frac{1}{10})$

$=\frac{2}{10}\times \frac{10}{9}$

$=\frac{2}{9}$