The significant figures (also called significant digits and abbreviated sig figs, sign.figs or sig digs) of a number are those digits that carry meaning contributing to its precision (see entry for Accuracy and precision). This includes all digits except:
- leading and trailing zeros (unless a decimal point is present) where they serve merely as placeholders to indicate the scale of the number.
- spurious digits introduced, for example, by calculations carried out to greater accuracy than that of the original data, or measurements reported to a greater precision than the equipment supports.
The concept of significant figures is often used in connection with rounding. Rounding to n significant figures is a more general-purpose technique than rounding to n decimal places, since it handles numbers of different scales in a uniform way. A practical calculation that uses any irrational number necessitates rounding the number, and hence the answer, to a finite number of significant figures. Computer representations of floating point numbers typically use a form of rounding to significant figures, but with binary numbers.
The term "significant figures" can also refer to a crude form of error representation based around significant figure rounding; for this use, see Significance arithmetic.
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