Hey there! I'm happy to help!
Let's say that our fraction is x.
x=0.5555555...
Let's get rid of the repeating stuff. If you multiplied x by 10, the fraction would be equal to 5.5555555.....
x=0.55555555....
10x=5.5555555.....
What if we subtracted the first equation from the second? Then all of the repeating stuff would be gone!
9x=5
We divide both sides by 9.
x=5/9.
Have a wonderful day! :D