Since you have *one* repeating digit, multiply by 10
10x = 8.777777
subtract the two equations. The repeating 7's will cancel out:
10x = 8.777777
...x = 0.877777
----------------------
9x = 7.9
Divide both sides by 9:
x = 7.9 / 9
multiply top and bottom by 10 to get rid of the decimal point:
x = 79 / 90
