key term - Relative error

Definition

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.

5 Must Know Facts For Your Next Test

1. Relative error is calculated as the absolute error divided by the true value: $\text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}}$.
2. It provides a dimensionless quantity, making it useful for comparing errors in measurements of different magnitudes.
3. In linear approximations, relative error can help assess the accuracy of an approximation function over an interval.
4. A smaller relative error indicates a more accurate measurement or approximation.
5. Relative error can be useful when dealing with very large or very small numbers, as it normalizes the error.

Review Questions

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 \(dx\).