# Significant Figures Calculator

This tool, The Significant Figures Calculator, lets users compute and edit significant figures.

The tool is based on the theory of relative errors and reports results in conventional and scientific notation. Values involving ambiguous trailing zeros are properly counted.

A handy tool for teachers and students, and for those that need to report quantities to a given number of significant figures.

Giving a precise definition for the correct number of significant figures is quite subtle (Higham, 2002). Different rules for counting significant figures have been reported. There is also the fact that not all significant figures are meaningful figures.

The theory of relative errors can be used to derive safe counting guidelines. See Numerical Analysis, by Burden and Faires, pages 20-22. According to the theory, it can be stated that significant figures can be attributed only to measured quantities for which a relative error can be computed. Thus it is not possible to attribute significant figures to zero as a quantity, exact numbers, conversion factors, and non-measured constants. However, all digits of a measured constant are significant.

Although there are many similar calculators out there, many do not pass what can be called “the test of zeros”. That is, enter one or more zeros as a quantity (0, 0.0, 0.00,…) and check the result. According to the theory of relative errors, no significant figures attribution is possible. Expressing these in scientific notation does not add any artificial significance to them as we still cannot compute relative errors for them.

Let us finally address the question of how many significant figures are in “0.”, i.e., in a zero followed by a decimal point. Some authors claim that this zero has one significant figure. Their argument here is that the convention of trailing zeros ending with a decimal place applies. This implies that said zero is trailing itself. This is an invalid argument as we can also imply that said zero is a leading zero, leading itself. Again, no relative error can be computed for a self-trailing or self-leading zero.

Last updated: 5-23-2021