Relative error is a measure of the uncertainty in a measurement compared to the size of the measurement itself. It is typically expressed as a percentage or fraction.
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Relative error is calculated as the absolute error divided by the true value: $\text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}}$.
It provides a dimensionless quantity, making it useful for comparing errors in measurements of different magnitudes.
In linear approximations, relative error can help assess the accuracy of an approximation function over an interval.
A smaller relative error indicates a more accurate measurement or approximation.
Relative error can be useful when dealing with very large or very small numbers, as it normalizes the error.
Review Questions
How do you calculate relative error?
Why is relative error considered dimensionless, and why is this important?
In what scenarios might you prefer to use relative error over absolute error?
Related terms
Absolute Error: The difference between the measured value and the true value of a quantity.
Linear Approximation: An approximation of a function using its tangent line at a specific point.
Differentials: \(dy\) represents an infinitesimally small change in \(y\) resulting from an infinitesimally small change in \(x\), denoted by \(dx\).