We emphasize that the completeness of the partition function, i.e. the use of a converged partition function at the typical temperature range of the survey, is very important to decrease the uncertainty on this quantity and thus to derive reliable interstellar molecular densities. In that context, we will show how the use of different approximations for the rovibrational partition function together with some interpolation and/or extrapolation procedures may affect the estimate of the interstellar molecular column density. For that purpose, we will apply the partition function calculations to astronomical observations performed with the IRAM-30m telescope towards the NGC7538-IRS1 source of the two following N-bearing molecules: isocyanic acid (HNCO, a quasilinear molecule) and methyl cyanide (CH_3_CN, a symmetric top molecule). The case of methyl formate (HCOOCH_3_), which is an asymmetric top O-bearing molecule which contains an internal rotor will also be discussed. Our analysis shows that the use of different partition function approximations leads to relative differences in the resulting column densities in the range of 9% up to 43%. Thus, we expect that this work turns out to be relevant for surveys of sources with temperatures higher than 300 K and to observations in the infrared.