Absolute Value

views updated May 18 2018

Absolute Value

Absolute value is an operation in mathematics, written as bars on either side of the expression. For example, the absolute value of 1 is written as |1|.

Absolute value can be thought of in three ways. First, the absolute value of any number is defined as the positive of that number. For example, |8| = 8 and |8| = 8. Second, one absolute value equation can yield two solutions. For example, if we solve the equation |x | = 2, not only does x = 2 but also x = 2 because |2| = 2 and |2| = 2.

Third, absolute value is defined as the distance, without regard to direction, that any number is from 0 on the real number line. Consider a formula for the distance on the real number line as |k 0|, in which k is any real number. Then, for example, the distance that 11 is from 0 would be 11 (because |11 0| = 11). Likewise, the absolute value of 11 is equal to 11. The distance for 11 will also equal 11 (because |11 0| = |11| = 11), and the absolute value of 11 is 11.

Thus, the absolute value of any real number is equal to the absolute value of its distance from 0 on the number line. Furthermore, if the absolute value is not used in the above formula |k 0|, the result for any negative number will be a negative distance. Absolute value helps improve formulas in order to obtain realistic solutions.

see also Number Line; Numbers, Real.

Michael Ota

absolute value

views updated May 23 2018

absolute value The magnitude of a number, regardless of its sign (positive or negative). For example, 25 is the absolute value of 25 and –25. Most spreadsheet programs include a function that returns the absolute value of a number.