On the Distributions of Significant Digits and Roundoff Errors Generalized logarithmic law is derived for the distribution of the first t significant digits of a random digital integer. This result is then used to determine the distribution of the roundoff errors in floating-point operations, which is a mixture of uniform and reciprocal distributions. CACM May, 1974 Tsao, N. significant digits, floating-point operations, roundoff errors, uniform distribution, reciprocal distribution, variance, mean valve 5.10 5.11 CA740504 JB January 17, 1978 4:12 PM 2649 5 2649 2649 5 2649 2649 5 2649