  Unimodular quantum cosmology admits wavepacket solutions that evolve
according to a kind of Schr\"odinger equation. Though this theory is equivalent
to general relativity on the classical level, its canonical structure is
different and the problem of time does not occur. We present an Ehrenfest
theorem for the long term evolution of the expectation value of the scale
factor for a spatially flat Friedmann universe with a scalar field. We find
that the classical and the quantum behaviour in the asymptotic future coincide
for the special case of a massless scalar field. We examine the general
behaviour of uncertainties in order to single out models that can lead to a
classical universe.
