I think the problem is meant to be 0.11012
To solve this problem, let's note something really important. We have
0.12=120.012=122=140.00012=124=116
This is important because notice that 0.1101=0.1+0.01+0.0001
So, now we just have 12+14+116=816+416+116=13/16
So 13/16 is our answer.
Thanks! :)