We calculate the condensate fraction and the condensate and noncondensate spatial and momentum distribution of the Bose-Hubbard model in a trap. From our results, it is evident that using approximate distributions can lead to erroneous experimental estimates of the condensate. Strong interactions cause the condensate to develop pedestal-like structures around the central peak that can be mistaken as noncondensate atoms. Near the transition temperature, the peak itself can include a significant noncondensate component. Using distributions generated from quantum Monte Carlo simulations, experiments can map their measurements for higher accuracy in identifying phase transitions and temperature.