Two-dimensional, direct numerical simulations of premixed turbulent combustion in the so-called flamelet regime were done in an earlier study. The flame "surfaces" passed through stationary isotropic turbulence that was maintained by forcing at either large scales (LS) or small scales (SS) producing inertial ranges with power-law exponents of -3 and -5/3, respectively. In the present study, the impact of the inertial range scaling on the fractal dimension of the flame surface is considered. It is shown that the SS simulations, having the more classical -5/3 inertial range, yield fractal dimensions that are in closer agreement with experimental measurements in the literature than the LS simulations with the -3 inertial range. Indeed, the latter produce consistently lower fractal dimensions than the SS simulations and experiment. A theoretical expression for the fractal dimension of an isocontour of a passive scalar developed by Vascillicos and Hunt does not compare favorably with the simulation results for the flame surface. We propose an alternative empirical expression (D-K = d - 0.42 - 0.15q, where d is the dimension of the system and q is the inertial range exponent) that agrees more closely with the simulation results, particularly at high turbulence intensities.