The correct answer is 193/990.
Explanation:
Let x=0.194949494...
This would make 10x=1.94949494... and 1000x=194.94949494....
Subtracting these, we have
(1000x-10x)=(194.949494-1.949494)
990x=193.
Divide both sides by 990:
990x/990 = 193/990
x=193/990.
