Aren significant digits good enough for precision calculations?
No. Significant digits are a crude measure of the uncertainty. Even when done correctly in simple calculations significant digits are crude. For example if we solve the simple equation 1.1 * 1.2 * 1.3 * 14. Significant digits misses the true uncertainty by nearly a factor of ten. The following table shows the different results. Answer Low High % Error Comment 24.024 24.024 24.024 0% Assume exact numbers 24. 23.5 24.5 4.2% Assume 2 significant digits 20.38 to 28.14 20.38 28.14 38.1% Using UnitMath The low estimate is 1.05 * 1.15 * 1.25 * 13.5 ~ 20.38 , and the high estimate is 1.15 * 1.25 * 1.35 * 14.5 ~ 28.14 . For information on making decimals exact see How can I make $49.95 exact? To put the above numbers into perspective, assume that you were calculating the cost of a project in millions of dollars. If you used significant digits you’d say that 25 million will cover the project with no problem. When the actual project is nearing completion you could find that you are several millio
