Question

What is 0.482 repeating as a simplified fraction? with the 82 reapeating

Answer 1

$x=0.4828282...\qquad\text{multiply both sides by 10}\\\\10x=4.82828282...\qquad\text{multiply both sides by 100}\\\\1000x=482.828282...\qquad\text{Make a difference}\\\\1000x-10x=482.828282...-4.828282...\\\\990x=478\qquad\text{divide both sides by 990}\\\\x=\dfrac{478:2}{990:2}\\\\\boxed{x=\dfrac{239}{495}}\\\\Answer:\ \boxed{0.4\overline{82}=\dfrac{239}{495}}$