You have 1.63636363636...
0.63636363636... is the repeating part. The first term of 0.63636363636... is 0.63, and the common ratio is 1/100.
a
Thus, the sum of the terms of this series is ----------
1 - r
which in this problem comes to:
0.63 63/100
------------------ = ---------------- = 63/99 = 7/11
1 - 1/100 99/100
And so, 1.63333333 ... = 1 + 7/11 or 18/11