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

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

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##