Definition
Absolute value
Absolute value is a number’s distance from zero on the number line.
What it means
Start at zero and count how many units it takes to reach the number. The direction does not matter for distance. Negative 6 is six units to the left of zero, and positive 6 is six units to the right, so both numbers have absolute value 6.
Remember it
Ask “How far from zero?”—not “Which way from zero?”
Example
A lift is on floor −4. Its floor number is four steps below ground level, so its distance from floor 0 is 4. Therefore |−4| = 4.
Watch for
Order and absolute value answer different questions. Although −8 is less than −3, |−8| is greater than |−3| because 8 is farther from zero than 3.
Common mix-up
“Make a negative number positive” may predict some answers, but it hides the meaning. Distance from zero also explains positive numbers and zero itself.
Exact meaning
The absolute value of a number is its non-negative distance from zero on the number line. The notation |a| means the absolute value of a.