Why is it that "all basic physical measurements [...] are ratios"? This question comes from the book Mathematical Physics by Donald H. Menzel. Here is the explanation given:
1. The significance of an observation. Any direct observation of a physical nature ordinarily results in a number expressing the magnitude of the measured quantity. The simpler measures are those of lengths, of masses, or of times. More complicated ones may be of velocities, of energies, or of angular momenta. The number, by itself, does not indicate what is being observed; its magnitude depends on the upon the type of measuring scale employed. We may express lengths in centimeters, miles, or light years; we may define masses in grams, tons, or in units of solar mass. All basic measurements are, therefore, ratios.