THE DISTRIBUTION OF LEADING SIGNIFICANT DIGITS

Most numbers which arc encountered arc the result of some arithmetic operations. The object of this paper is to show why their leading significant digits are not uniformly distributed. It has long been surmised that the distribution of leading significant digits is logarithmic. Indeed this is already known under the assumption of invariance to scaling. In this paper we establish this distribution without any such assumption, and thus that over 30% of decimal numbers can be expected to have leading significant digit 1. © 1982 Academic Praj Inc. (London) Limited.