A basic consequence of Mostow-Prasad Rigidity is that if M=H^3/G is an orientable hyperbolic 3-manifold of finite volume, then the traces of the elements in $\G$ are algebraic numbers. Say that M has non-integral trace if G contains an element whose trace is an algebraic non-integer. This talk will consider manifolds with non-integral trace and show for example, that there are infinitely many non-homeomorphic hyperbolic knot complements S^3\ K_i with non-integral trace.