Looks like this is meant to be: 0.0002020202....
So let x = 0.0002020202...
Then 100x = 0.0202020202...
Subtract the first from the second: 99x = 0.02, so x = 0.02/99
Multiply numerator and denominator by 100: x = 2/9900
Simplify: x = 1/4950