What absolute value means
The absolute value of a number is its distance from zero on the number line, so it is never negative. Written |x|, it equals x when x is zero or positive and −x when x is negative: |8| = 8 and |−8| = 8.
The absolute difference |a − b| is the distance between a and b. Because distance has no direction, |a − b| = |b − a|.
Worked examples
|−7.25|: the number is negative, so |−7.25| = −(−7.25) = 7.25.
|3.5 − (−12)|: first a − b = 3.5 + 12 = 15.5, then |15.5| = 15.5. Swapping the order gives −12 − 3.5 = −15.5, whose absolute value is also 15.5.
Exact decimals
The calculator subtracts as exact decimals rather than binary floating point, so |0.3 − 0.1| comes out as exactly 0.2 instead of 0.19999999999999998.