Question

Can someone help me simplify 0.482 into a simplified fraction and the number is repeating.

Answer 1

482/999

Explanation:

Since there are 3 repeating digits, starting at the decimal point, the short answer is that the fraction is ...

482/999

where 999 has a number of 9's equal to the number of repeating digits.

This fraction cannot be reduced.

_____

Long answer

Multiply the value by 1000 = 10^3, where the '3' is the number of repeating digits. Then subtract the original and divide by the coefficient of 'x'.

`x=0.\overline{482}\\1000x=482.\overline{482}\\1000x-x=482.\overline{482}-0.\overline{482}\\999x=482\\\\x=(482)/(999)`

482 and 999 have no common factors, so the fraction cannot be reduced.