Well i think the topic and my solution has made the forum hot and invited lot of arguments. But its good to see that such forum can be highly interactive to such an appreciable extent like a lively classroom type situation.
The first term for x is irrational and second is rational for it can be reduced to p/q form where p and q are integers and q is non zero as follows:
Second term is = 0.27272727...
let this be a rational no.
so p/q = 0.2727272727... ----(1)
or 100p/q = 27.27272727.... -----(2)
subtracting (1) from (2) we obtain
99p/q = 27
or p/q = 0.27272727.... = 27/99
thus the second term is rational. Had it not been so we would have arrived at contradiction which in turn would suggest that our assumption is wrong and thus we are forced to consider the term in other way.
I was unable to obtain the p/q form for first term so i considered it as irrational.