  The Kochen-Specker theorem states that noncontextual hidden variable models
are inconsistent with the quantum predictions for every yes-no question on a
qutrit, corresponding to every projector in three dimensions. It has been
suggested [D. A. Meyer, Phys. Rev. Lett. 83, 3751 (1999)] that the
inconsistency would disappear when we are restricted to projectors on unit
vectors with rational components; that noncontextual hidden variables could
reproduce the quantum predictions for rational vectors. Here we show that a
qutrit state with rational components violates an inequality valid for
noncontextual hidden-variable models [A. A. Klyachko et al., Phys. Rev. Lett.
101, 020403 (2008)] using rational projectors. This shows that the
inconsistency remains even when using only rational vectors.
