How can I develop a pseudo-polynomial time algorithm for a non-integer problem?

Question

I have an scheduling probelm with a set of jobs $J$, with a ''non-integer'' parameter $\beta_j$, i.e. the parameter is a real number and $\beta_j \leqslant 0.5, \exists j \in J$.

Since the problem will be trivial if $\beta_j > 0.5, \forall j \in J$, I can not assume that we may transform an instance to an integer one. By the way, I am looking for the computational complexity of the problem.

So my question is: How can I develop a pseudo-polynomial time algorithm for the problem (to indicate that it is at most NP-hard in the ordinary sense), although the problem is not integer-value?