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The diverse applications of the Benford law attract investigators working invarious fields of physics, biology and sociology. At the same time, thegroundings of the Benford law remain obscure. Our paper demonstrates that theBenford law arises from the positional (place-value) notation accepted forrepresenting various sets of data. An alternative to Benford formulae topredict the distribution of digits in statistical data are derived. Applicationof these formulae to the statistical analysis of infrared spectra of polymersis presented. Violations of the Benford Law are discussed.

Intuitive Considerations Clarifying the Origin and Applicability of the Benford Law