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We demonstrate how one should transform correctly quasi-isotropic coordinatesto Weyl-Papapetrou coordinates in order to compare the metric around a rotatingstar that has been constructed numerically in the former coordinates with anaxially symmetric stationary metric that is given through an analytical form inthe latter coordinates. Since a stationary metric associated with an isolatedobject that is built numerically partly refers to a non-vacuum solution(interior of the star) the transformation of its coordinates to Weyl-Papapetroucoordinates, which are usually used to describe vacuum axisymmetric andstationary solutions of Einstein equations, is not straightforward in thenon-vacuum region. If this point is \textit{not} taken into consideration, onemay end up to erroneous conclusions about how well a specific analytical metricmatches the metric around the star, due to fallacious coordinatetransformations.

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics