Interpret absolute value as distance and use it to compare quantities and errors.
Compare errors or deviations with absolute value
Problem
A machine is supposed to cut metal rods to \(50~\text{cm}\). \(\text{One}~\text{rod}\) is \(52~\text{cm}\) and another is \(45~\text{cm}\). Calculate each rod's absolute error from the target and determine the more accurate rod.
Big Picture
What this problem is really about
Use the target length as the common reference instead of comparing the rods directly. Find each rod’s absolute difference from fifty centimeters, which puts an overcut and an undercut on the same nonnegative error scale. The rod with the smaller absolute error is more accurate, and both error sizes should accompany that conclusion.
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