Question

How do you convert 0.7 (7 being repeated) to a fraction?

Answer 1

`0.bar(7) = 7/9`

Explanation:

With the notation of using a bar to denote a repeating digit,

let `x = 0.bar(7)`

`=> 10x = 7.bar(7)`

`=>10x - x = 7.bar(7)-0.bar(7)`

`=>9x = 7`

`=>x = 7/9`

This technique works in general to find the fractional representation of a repeating decimal. Just multiply by `10^n` where `n` is the number of digits that are repeating, then subtract away the original repeating digit and solve for `x`.