  We present a fully-differential and high-precision calculation of top-quark
pair-production and decay at the LHC, providing predictions for observables
constructed from top-quark leptonic and $b$-flavoured jet final states. The
calculation is implemented in a parton-level Monte Carlo and includes an
approximation to the next-to-next-to leading order (NNLO) corrections to the
production and, for the first time, the exact NNLO corrections to the decay
subprocesses. The corrections beyond NLO are sizeable, and including them is
crucial for an accurate description of the cross section constrained by
experimental phase-space restrictions. We compare our predictions to published
ATLAS and CMS measurements at the LHC, finding improved agreement compared with
lower orders in the perturbative expansion.
