How do you convert decimals with bar into fraction?

Answer 1

First let N = the number that you want to convert. Now multiply the number by a power of ten based on the quantity of digits that repeat. So if 1 digit repeats, multiply by 10^1 = 10. If 2 digits repeat, multiply by 10^2 = 100, etc. Subtract the original from the new. So you will have something like 10N - N = 9N = (some number), or 100N - N = 99N = (a number). Then divide both sides by 9 or 99 or whatever you have, then you have N = (something)/99, etc. Simplify the fraction.

Example: N = 0.83333..... [one digit repeats] --> 10N = 8.33333....

10N - N = (8.33333.....) - (0.83333....) = 7.5, so 9N = 7.5 --> 90N = 75.

N = 75/90 = 5/6

One more example: N = 0.0909.... ; 100N = 9.0909....

100N - N = (9.0909...) - (0.0909...)

99N = 9 ---> N = 9/99 = 1/11