OPTIMAL NUMBER OF DIGITS TO REPORT

Abstract

Instrumentation, computation, and documentation often involve the task of reporting a number with an indicator of its possible error. For quick decision making, reporting only one number with reliable digits is more desirable than reporting two or more numbers with insignificant lower digits. This paper proposes an optimal method to determine the number of digits to report. The method is free of arbitrary thresholds unlike the customary representation by confidence interval and other existing methods. The model used to derive the method is based on the observation that the amount of ignorance regarding the value of a number's lower digits may be expressed by a uniform distribution. If the number to report is accompanied by its standard error, the problem of deciding the number of digits to report reduces to matching the level of ignorance by approximating a normal distribution by the uniform distribution. The goodness of the approximation is measured in terms of the Kullback-Leibler information, which is minimized.