  The grazing limit of the Boltzmann equation to Landau equation is well-known
and has been justified by using cutoff near the grazing angle with some
suitable scaling. In this paper, we will provide a new understanding by simply
applying a natural scaling on the Boltzmann operator without angular cutoff.
The proof is based on a new well-posedness theory on the Boltzmann equation
without angular cutoff in the regime with optimal ranges of parameters so that
the grazing limit can be justified directly for any $\gamma>-5$ that includes
the Coulomb potential corresponding to $\gamma=-3$. With this new
understanding, the scaled Boltzmann operator in fact can be decomposed into two
components. The first one converges to the Landau operator when the singular
parameter $s$ of interaction angle tends to $1^{-}$ and the second one vanishes
in this limit.
