Question

How do you convert 0.03 (3 repeating) to a fraction?

Answer 1

`0.0bar(3) = 1/30`

Explanation:

As a general method for converting repeating decimals to fractions, suppose that the repeating portion is `n` digits long. Then let `x` represent the initial value, and using the fact that `10^nx-x` has finitely many digits, solve for `x` to find the fraction.

In this case, `3` is the repeating portion, which has `1` digit. Thus, we will let `x=0.0bar(3)` (the bar denotes repeating digits) and multiply by `10^1`.

`x = 0.0bar(3)`

`=>10x = 0.bar(3)`

`=>10x-x = 0.bar(3)-0.0bar(3)`

`=> 9x = 0.3`

`=> x = 0.3/9 = 3/90 = 1/30`