Musing on Use and Misuse of Numerical Data of Quantities in Measurement Science

Abstract

The empirical numerical value of a quantity is not a number that can be treated as a simple mathematical object. The digits are not only determined by the chosen reference, but also by the full process that allowed setting them. The evaluation not only is affected by uncertainty, but the uncertainty level can be chosen from many “levels of confidence.” The latter establishes the degree of possibility that the available numerical value is reasonably acceptable as the actual numerical value of the quantity in question. Consequently, there are different ways to treat the digits of the same numerical values expressing the magnitude of the same quantity. This paper illustrates the above issues by using as examples the “fundamental constants” proposed for use in the new SI definition: Planck, Boltzmann, electrical charge, and Avogadro.