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I learned to keep track of the conversion from SI to Gaussian units for electromagnetism as \begin{align} \frac{e^2}{[4\pi\epsilon_0]} &= \alpha \hbar c \end{align} where the factor in [brackets] is unity in CGS units and isn't in SI. This is a nice way to remember things because it makes clear that Coulomb's law for two fundamental charges,  \vec F = ...