Question

Express the following as a rational number i.e. in the form $\frac{a}{b};$ where a, $b\in I$ and $b\ne 0.$

$0.\overline{285714}$

• A. $\frac{2}{9}$
• B. $\frac{2}{7}$
• C. $\frac{2}{3}$
• D. $\frac{2}{5}$

Answer 1

The correct option is B $\frac{2}{7}$

$x=\mathrm{0.285714285714........}$.........(1)

$10,00,000x=\mathrm{285714.285714....}$.......(2)

Subtarct (1) from(2)

$999999x=285714$

$x=\frac{285714}{999999}$

$x=\frac{2}{7}$