Write the following infinite decimal expansion as a fraction. You do not need to simplify.
0.111...
Let x = 0.111...
Multiply both sides of the equation by 10:
10x = 1.111...
Subtracting x from both sides:
(10x - x) = (1.111... - 0.111...)
9x = 1
Divide both sides by 9:
x = 1/9
Therefore, the fraction representation of the infinite decimal expansion 0.111... is 1/9.