  Identifying the relativistic multipole moments of a spacetime of an
astrophysical object that has been constructed numerically is of major
interest, both because the multipole moments are intimately related to the
internal structure of the object, and because the construction of a suitable
analytic metric that mimics a numerical metric should be based on the multipole
moments of the latter one, in order to yield a reliable representation. In this
note we show that there has been a widespread delusion in the way the multipole
moments of a numerical metric are read from the asymptotic expansion of the
metric functions. We show how one should read correctly the first few multipole
moments (starting from the quadrupole mass-moment), and how these corrected
moments improve the efficiency of describing the metric functions with analytic
metrics that have already been used in the literature, as well as other
consequences of using the correct moments.
