First, four-digit precision of power calculations may be mandatory in many applications. For example, both compromise power analyses for very large samples, and error probability adjustments in case of multiple tests of significance may result in very small values of $\alpha$ or $\beta$ (Westermann & Hager, 1986).
Source:
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175-191.
From the G*Power paper:
Source: Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175-191.