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Significant figure

From Encyclopedia of Mathematics
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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
How to Cite This Entry:
Significant figure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Significant_figure&oldid=48697
This article was adapted from an original article by Kh.D. Ikratov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article