The significant figures 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 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 r
ounding to n decimal places, since it handles numbers of different scales in a uniform way. For example, the population of a city might only be known to the nearest thousand and be stated as 52,000, while the population of a country might only be known to the nearest million and be stated as 52,000,000. The former might be in error by hundreds, and the latter might be in error by hundreds of thousands, but both have two significant figures (5 and 2). This reflects the fact that the significance of the error (its likely size relative to the size of the quantity being measured) is the same in both cases.
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.
