IBMathsDPApplications & Interpretation (AI)SLRevision Notes1. Number & AlgebraNumber ToolkitPercentage Error

Percentage Error (DP IB Applications & Interpretation (AI): SL): Revision Note

Written by: Amber

Reviewed by: Mark Curtis

Updated on 27 November 2025

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Percentage error

What is percentage error?

Percentage error is a measure of how far away an estimated (or rounded) value is from the actual (or exact) value
- Percentage error, $ε$ , can be calculated using the formula $ε = | \frac{v_{A} - v_{E}}{v_{E}} | \times 100 %$
  - where $v_{E}$ is the exact value
  - and $v_{A}$ is the approximate value of $v_{E}$
- The | | means take the absolute value (the positive value)
  - e.g. $| - 5 | = 5$
  - Percentage errors should always be positive
The further away the estimated answer is from the true answer, the greater the percentage error

Examiner Tips and Tricks

The percentage error formula is given in the formula booklet.

Worked Example

Let $P = x \cos (2 y)$ , where $y = 15 °$ and $x = 4$ .

(a) Calculate the exact value of $P$ .

Answer:

(b) Calculate the percentage error when using an estimate of 3.5 for the value of $P$ .

Answer:

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