Significant figure

significant digit

A term pertaining to the approximate specification of a real number. Let a real number be represented in a number system with base by a -ary fraction

In this notation, suppose that is the first non-zero digit, counted from the left. Then all subsequent digits are called significant digits of the approximate number .

A significant digit is said to be correct if the absolute error of , i.e. the difference , satisfies the inequality

In approximate specification of a real number it is usually meaningful to specify only significant digits.

Comments

One speaks of doing a calculation to three significant digits if each calculated result is rounded so that there are no more than three digits after and including the first non-zero digit. One says that an approximate number resulting from a calculation (in mathematics) or from a measurement (in sciences and technology) with significant digits is correct to significant digits, , if the error

is less than . Usually or . For example, is the correct answer to three significant digits of .

References

[a1]	D.M. Young, R.T. Gregory, "A survey of numerical mathematics" , I , Dover, reprint (1988) pp. Chapt. 1