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approximate equality

Approximate equality is a concept used primarily in physics and engineering, and also occasionally in mathematics. Two quantities are approximately equal when they are close enough in value so the difference is inconsequential in practical terms. Approximate equality is symbolized by a squiggly equal sign ( ).

As an example of how approximate equality can be used in mathematics, consider the positive square root of 2 (or 2 1/2 ). This is an irrational number ; when written in decimal form, it is nonterminating and nonrepeating. Expressed to four significant digits, 2 1/2 1.414. It is possible to express it to many more significant digits, but the result will always be an approximation. Thus, to 10 significant digits, 2 1/2 1.414213562, and to 20 significant digits, 2 1/2 1.4142135623730950488. An example of an approximate equation using variables is x + y z .

In experimental physics and engineering, approximate equality is the rule, because measurements of physical quantities and phenomena are seldom exact. We might say, for example, that an incandescent lamp consumes a power P of approximately 60 watt s (60 W); then we can write P 60 W. Or we might say that the speed S of a computer-file download is approximately 38.3 kilobit s per second (kbits/sec); we would then write S 38.3 kbits/sec.

In many cases, the ordinary equality symbol (=) is used in situations where, to be rigorous, the approximate equality sign ought to be used. This is done for two reasons: first, most fonts do not include an approximate equality symbol; and secondly, many people do not know what the approximate equality symbol means.

Also see Mathematical Symbols .

This was last updated in September 2005
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