The vacuum impedance and unit systems

In electromagnetism, the vacuum impedance $Z_0$ is a universal constant, which is as important as the velocity of light $c$ in vacuum. Unfortunately, however, its significance does not seem to be appreciated so well and sometimes the presence itself is ignored. It is partly because in the Gaussian system of units, which has widely been used for long time, $Z_0$ is a dimensionless constant and of unit magnitude. In this paper, we clarify that $Z_0$ is a fundamental parameter in electromagnetism and plays major roles in the following scenes: reorganizing the structure of the electromagnetic formula in reference to the relativity; renormalizing the quantities toward natural unit systems starting from the SI unit system; and defining the magnitudes of electromagnetic units.