The direct method for Absolute Value
Evaluate anything inside the absolute-value bars, locate that result on a number line, and read its distance from zero. A nonnegative result stays the same; a negative result is replaced by its opposite.
Absolute value measures distance on the number line. Distance has no direction, so |−14.6| and |14.6| are both 14.6 even though the original numbers lie on opposite sides of zero. For a connected concept in Absolute Value, see coordinate distance.
Using Absolute Value in later work
Signed quantities turn up in temperatures, elevations, account changes, coordinates, and measurement errors. Absolute value is useful when the size of the difference matters more than whether the change was upward or downward.
A temperature moves from 3°C to −5°C. The signed change is −8°C, while the magnitude of that change is |−8| = 8°C. Those statements answer different questions. This Absolute Value example can be compared with absolute error in a percentage.
Checks that protect a Absolute Value result
Do not remove a negative sign before completing the expression inside the bars. For |4 − 11|, subtract first to get |−7|, then report 7. Also remember that −|6| is −6 because the outside minus remains.
Interpreting changes in Absolute Value
How to label a Absolute Value result
Absolute value is not the same as deleting every minus sign in a longer expression. It applies only to the expression enclosed by the bars after that expression has been evaluated. Here the requested quantity is specifically absolute value.
Keep the supplied input with the result, including any units and the final rounding place. The displayed formula then preserves how the absolute value was obtained.
Validating Absolute Value
Check Absolute Value from Number, then verify the fixed condition. Estimate the Absolute Value Absolute value before computing it again. If the fixed condition changes during Absolute Value, keep the fixed condition fixed. That Absolute Value comparison shows whether Absolute value moves as expected.
A simple Number supplies a benchmark for Absolute Value. Retain the fixed condition and predict Absolute value. The benchmark helps distinguish an unlikely Absolute Value magnitude from ordinary rounding in Absolute value.