Question

How do you convert 0.6 (6 being repeated) to a fraction?

Answer 1

`0.bar(6) = 2/3`

Explanation:

Multiply by `10` to shift one place to the left and subtract the starting number to cancel out the repeating decimal.

To do this multiply by `(10-1)`:

`(10-1) * 0.bar(6) = 6.bar(6) - 0.bar(6) = 6`

Then divide both sides by `(10-1)` to find:

`0.bar(6) = 6/(10-1) = 6/9 = (color(red)(cancel(color(black)(3)))*2)/(color(red)(cancel(color(black)(3)))*3) = 2/3`