Interpret absolute value as distance and use it to compare quantities and errors.
Choose a smart strategy for absolute value and distance
Problem
What is the most useful first step for comparing how far \(-4\) and \(2.5\) are from \(0\): compare the signed numbers, find each distance from \(0\), or subtract \(\text{one}~\text{number}\) from the other? Use that step to identify the number farther from \(0\) and the difference between their distances.
Big Picture
What this problem is really about
The reference point is zero, so begin by finding each number’s absolute value rather than comparing signed order or finding the span between the numbers. Compare those two distances to identify the farther original number. Then subtract the smaller distance from the larger to determine how much farther it is.
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