The Distribution of Leading Significant Digits
PETER R. TURNER · IMA Journal of Numerical Analysis · 1982
Most numbers which are encountered are 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.