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.
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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 \(dx\).