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
DC
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