Significant Digits

When a number is expressed in scientific notation, the number of significant digits (or significant figures) is the number of digits needed to express the number to within the uncertainty of calculation. For example, if a quantity is known to be 1.234+/-0.002, four figures would be significant

The number of significant figures of a multiplication or division of two or more quantities is equal to the smallest number of significant figures for the quantities involved. For addition or subtraction, the number of significant figures is determined with the smallest significant figure of all the quantities involved. For example, the sum 10.234+5.2+100.3234 is 115.7574, but should be written 115.8 (with rounding), since the quantity 5.2 is significant only to +/-0.1.

See also

Accuracy, Fractional Part, Integer Part, Least Significant Bit, Nearest Integer Function, Precision, Rounding, Significance Arithmetic, Truncate

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References

Kenney, J. F. and Keeping, E. S. "Significant Figures." §1.5 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 8-9, 1962.Mulliss, C. "Significant Figures and Rounding Rules." http://www.angelfire.com/oh/cmulliss/.

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Significant Digits

Cite this as:

Weisstein, Eric W. "Significant Digits." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SignificantDigits.html

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