  The scattering of fast radio bursts (FRBs) by the intergalactic medium (IGM)
is explored using cosmological hydrodynamical simulations. We confirm that the
scattering by the clumpy IGM has significant line-of-sight variations. We
demonstrate that the scattering by the IGM in the voids and walls of the cosmic
web is weak, but it can be significantly enhanced by the gas in clusters and
filaments. The observed non-monotonic dependence of the FRB widths on the
dispersion measures (DM) cannot determine whether the IGM is an important
scattering matter or not. The IGM may dominate the scattering of some FRBs, and
the host galaxy dominates others. For the former case, the scattering should be
primarily caused by the medium in clusters. A mock sample of 500 sources shows
that $\tau_{\rm{IGM}} \propto \rm{DM_{IGM}}^{1.6-2.1}$ at $z<1.5$. Assuming
that the turbulence follows Kolmogorov scaling, we find that an outer scale of
$L_0\sim 5\,$pc is required to make $\tau_{\rm{IGM}} \sim 1-10\,$ms at $\nu=1\,
$ GHz. The required $L_0\sim 5\, $pc can alleviate the tension in the
timescales of turbulent heating and cooling but is still $\sim 4$ orders of
magnitude lower than the presumed injection scale of turbulence in the IGM. The
gap is expected to be effectively shortened if the simulation resolution is
further increased. The mechanisms that may further reduce the gap are shortly
discussed. If future observations can justify the role of the IGM in the
broadening of FRBs, it can help to probe the gas in clusters and filaments.
