How many digits in a mean are worth reporting?

Most bioscientists need to report mean values, yet many have little idea of how many digits are significant, and at what point further digits are mere random junk. Thus a recent report that the mean of 17 values was 3.863 with a standard error of the mean (SEM) of 2.162 revealed only that none of the seven authors understood the limitations of their work. The simple rule derived here by experiment for restricting a mean value to its significant digits (sig-digs) is this: the last sig-dig in the mean value is at the same decimal decade as the first sig-dig (the first non-zero) in the SEM. An extended rule for the mean, and a different rule for the SEM itself are also derived. For the example above the reported values should be a mean of 4 with SEM 2.2. Routine application of these simple rules will often show that a result is not as compelling as one had hoped.