By this paper the author shows, that the transformation of the fundamental physical constants c, G, h, e und kc into systems of units, which differ fundamentally from the International System of Units (SI), is a powerful tool to free the numeric values of the constants from their arbitrariness, caused by the historical choice of units. The arbitrariness of units means not at all the careful definition, harmonisation and calibration of units by the international metrological community but the arbitrary scaling of the size of units in the physical sense. By transferring the fundamental physical constants into systems of units, with extraordinary scales (e.g. Planck scale) or natural scales like the Proton´s dimensions or the value of the Hubble constant one can show the true character of the fundamental physical constants. Such transformations uncover correlations - being searched for a long time – between the important dimensionless constants, such as α = 1/137,036 or mp/me = 1836,15 on the one hand and the constants with dimensions on the other hand. All in all the paper describes a lot of (numeric) correlations, which could help to find new physical understanding. Apart from that promising fact, the interconnections between the various systems of units and the underlying principles are very revealing, because one should know the effects of changing the physical scales.