Optimal number of digits to report

Instrumentation, computation, and documentation often involve the task of reporting a number with an indicator of its possible error. This paper proposes a method to determine the number of digits to report in such a situation, substituting the customary representation by confidence interval. The method has an optimal property and is free of arbitrary threshold. The model used to derive the method is based on the observation that the ignorance on the values of the lower digits of a number may be expressed by a uniform distribution. If the number to report is accompanied with 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 Kullback-Leibler information, which is to be minimized.