  Noncommutative surfaces finite over their centres can be realised as orders
over surfaces. The aim of this paper is to present a noncommutative
generalisation of rational singularities, which we call numerical rationality,
for such orders. We show that numerical rationality is independent of the
choice of resolution. Our main result is that the log terminal orders arising
from the noncommutative minimal model program, in particular, canonical orders
are numerically rational. Both of these generalise well known facts about
rational singularities in commutative algebraic geometry.
