Significant Figures

The significant figures (also known as significant digits, and often shortened to sig figs) of a number are those digits that carry meaning contributing to its precision. This includes all digits except:

• leading and trailing zeros which are merely placeholders to indicate the scale of the number.
• spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.

Inaccuracy of a measuring device does not affect the number of significant figures in a measurement made using that device, although it does affect the accuracy. A measurement made using a plastic ruler that has been left out in the sun or a beaker that unbeknownst to the technician has a few glass beads at the bottom has the same number of significant figures as a significantly different measurement of the same physical object made using an unaltered ruler or beaker. The number of significant figures reflects the device's precision, but not its accuracy.

The basic concept of significant figures is often used in connection with rounding. Rounding to 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. 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 number of correct significant figures is closely related to the notion of relative error (which has the advantage of being a more accurate measure of precision, and is independent of the radix of the number system used).

The term "significant figures" can also refer to a crude form of error representation based around significant-digit rounding; for this use, see significance arithmetic.