Why is the relative error, and not the absolute one, the meaningful quantity? Because the same discrepancy in absolute value may be negligible or disastrous depending on how much is being measured.
Example — The same error counts differently
Two scales both make an error of g.
- Weighing kg of flour: relative error (irrelevant).
- Weighing g of saffron: relative error (catastrophic).
The same absolute error may be acceptable or disastrous depending on the reference: this is why the relative error is the meaningful quantity for judging the quality of a measurement. We shall return to it when dealing with significant figures and error propagation in physics.
An error of g is insignificant on a kilo of flour but enormous on five grams of saffron. It is the ratio to the reference, that is, the relative error, that establishes whether a measurement is reliable.
Links
Topics: Percentages
Concepts: Absolute error · Relative error
Methods: Relative percentage error
Skills: Calculating · Reasoning by cases