Improved $u'g'r'i'z'$ to $UBVR_CI_C$ Transformation Equations for Main Sequence Stars

We report improved transformation equations between the $u'g'r'i'z'$ and $UBVR_CI_C$ photometric systems. Although the details of the transformations depend on luminosity class, we find a typical rms scatter on the order of 0.001 magnitude if the sample is limited to main sequence stars. Furthermore, we find an accurate transformation requires complex, multi-color dependencies for the bluer bandpasses. Results for giant stars will be reported in a subsequent paper.