It is shown that the symbols for the fundamental units of mechanics, namely length, time and mass, are capable of a meaningful interpretation as positive real parameters. Then a suitable parameter domain allows one to take the derived units into account. The formal manipulations usually carried out with symbols of physical quantities, involving real coefficients and units of different kinds affected by rational exponents, are consistent with that interpretation. The note is expected to serve as a well-motivated introduction to a deeper study of dimensional analysis.