Percentage error

Definition

Percentage error measures the accuracy of an approximate value compared to an exact value. It is expressed as a percentage and calculated using the formula $\left( \frac{\text{approximate value} - \text{exact value}}{\text{exact value}} \right) \times 100\%$.

5 Must Know Facts For Your Next Test

1. Percentage error provides insight into the relative accuracy of approximations derived from linear approximations and differentials.
2. A small percentage error indicates a high level of accuracy in the approximation.
3. Linear approximations are often used to estimate values, and the percentage error helps quantify how close these estimates are to actual values.
4. Calculating percentage error involves both the approximate and exact values; it’s essential to know both to determine the error.
5. Differentials can be used to find approximate changes, which can then be compared with actual changes using percentage error.

Review Questions

Related terms

Linear Approximation: An estimation method using the tangent line at a point to approximate function values near that point.

Differentials: Small changes in variables used to approximate changes in function values.

$\Delta x$ (Delta x): $\Delta x$ represents a small change or increment in the variable $x$.