Appropriate numerical precision

The art of reporting numbers with exactly as many significant figures as your measurement or model justifies—no more, no less. Excessive precision creates false confidence; insufficient precision loses information.

A measured distance of 5.2 meters shouldn't be written as 5.200000 m. Conversely, rounding a surveyed coordinate to the nearest kilometer discards crucial data. Context determines the boundary: a comet's orbital period needs fewer decimal places than a neural signal's timing.

The principle applies across domains. In psychological studies, reporting effect sizes to three decimal places misleads when sample sizes are small. In chemical kinetics, transition probabilities derived from limited data shouldn't claim more precision than the underlying data structure supports. Continuous functions in proofs demand exact symbolic form, not decimal approximations.

Feedback from peers and stakeholders helps calibrate. Too-loose reporting invites skepticism; too-tight reporting wastes reader attention and suggests overconfidence in intuitive or computational accuracy.

The sweet spot balances causal clarity with honest uncertainty.

Related

Significant figures, Uncertainty quantification, Rounding, Scientific notation, Statistical inference