Question

Express $0.\overline{38}$ as a rational number in simplest form.

Answer 1

$x=0.\overline{38}$

Let $x=0.3838$ (1)

Multiply both side by 100,

$100x=\mathrm{38.3838........}$ (2)

(2) –(1)

$100x-x=\mathrm{38.3838............}-\mathrm{0.3838.........}$

$99x=38$

$x=\frac{38}{99}$