Question 9346
.45 with a line over the top of it actually means the repeating decimal: .4545454545454545. . .


To find the fraction that it represents, 

let x = .4545454545 . . .


Multiply both sides of this equation by 10 for each digit that repeats.  If a single digit repeats, multiply by 10, if two digits repeat (as in this case), multiply both sides by 100, if three digits repeat, multiply by 1000.


100x = 45.45454545 . . .


Now subtract the x= .45454545 . . . from each side:


100x = 45.45454545 . . .
- x =  - .45454545 . . .


The result is
99x = 45
so x = {{{45/99 = 5/9}}}


R^2 at SCC