Dissipative particle dynamics (DPD) as a model of fluid particles suffers from the problem that it has no physical scale associated with the particles. Therefore, a DPD simulation requires an ambiguous fine-tuning of the model parameters with the physical parameters. A corrected version of DPD that does not suffer from this problem is smoothed dissipative particle dynamics (SDPD) [P. Espanol and M. Revenga, Phys. Rev. E 67, 026705 (2003)]. SDPD is, in fact, a version of the well-known smoothed particle hydrodynamics method, albeit with the proper inclusion of thermal fluctuations. Here, we show that SDPD produces the proper scaling of the fluctuations as the resolution of the simulation is varied. This is investigated in two problems: the Brownian motion of a spherical colloidal particle and a polymer molecule in suspension.