Prove that 0.565656.... can be expressed as 56/99.

1) Let x=0.565656...

2) Thus 100x=56.565656...

3) Subtracting equation 1) from 2) gives:

99x=56

4) Rearrange for x:

x=56/99, Also x=0.565656... from 1)

Therefore 0.565656...=56/99