Year 9 Mathematics · AC9M9M04

Absolute, Relative and Percentage Measurement Error

Every measured value is an estimate. Absolute error describes a difference in units; relative and percentage error scale that difference against the size of the quantity

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Learning goalsSay it simply

Every measured value is an estimate. Absolute error describes a difference in units; relative and percentage error scale that difference against the size of the quantity.

By the end of this lesson, you should be able to:

  • calculate absolute error
  • calculate relative error
  • convert relative error to percentage error
  • interpret accuracy in realistic measurement contexts
Key conceptTeach from the board

Absolute error has the original unit

Absolute error=|measured−reference|.

Relative error compares error with size

Relative error=absolute error/|reference value| when a meaningful reference is available.

Percentage error is relative error ×100%

It allows errors from different-sized measurements to be compared fairly.

Precision and accuracy are not identical

More decimal places can indicate finer resolution, but systematic bias can still make a precise measurement inaccurate.

Worked examplesWe do

Worked examples

AC9M9M04 - Absolute, Relative and Percentage Measurement Error
Example 1

Absolute error Measured 9.8 cm, accepted 10.0 cm → |9.8−10.0|=0.2 cm.

Example 2

Percentage error 0.2/10.0×100%=2%.

Example 3

Compare errors An error of 1 cm is minor on 10 m but large on 5 cm; relative error captures this.

Example 4

Rounding interval 12.4 cm to the nearest 0.1 cm represents values from 12.35 cm up to but not including 12.45 cm.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M9M04: calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates

Victoria: VC2M9M04 — Level 9 Measurement. The mapping names direct Level 9 content where available and explicitly identifies supporting content where the Victorian structure separates an idea differently.

NSW: Stage 5 measurement applications with Working mathematically; accuracy is embedded rather than a direct standalone equivalent. NSW organises Years 7–10 Mathematics through Stage 5 Core content groups and Paths rather than a one-code-per-Year-9 structure, so this lesson does not force a false one-to-one outcome.

Lesson componentAustralian CurriculumVictoriaNSW
Concept teaching + worked examplesAC9M9M04VC2M9M04 — Level 9 MeasurementStage 5 measurement applications with Working mathematically; accuracy is embedded rather than a direct standalone equivalent
Guided + independent practiceApplies the descriptor through progressively less-scaffolded problemsBuilds the corresponding Level 9 mathematical knowledge and fluencySupports Stage 5 Core/Path application and Working mathematically
Reasoning + assessment + masteryChecks transfer, justification, interpretation and model limitsChecks Level 9 reasoning at the mapped content depthChecks relevant Stage 5 reasoning without claiming a false Year 9 equivalent
Questions and answersWith answers
What is absolute error?
The magnitude of the difference between measured and reference values.
Why use relative error?
It compares error fairly across quantities of different sizes.
Can repetition remove systematic error?
No. Repetition helps reveal random variation; calibration or design addresses systematic bias.
Practice and reviewReady for practice
  • Percentage error=absolute error×100: Divide by the reference value first.
  • Absolute error can be negative: Error magnitude is non-negative.
  • More decimals guarantee accuracy: They may show precision, not freedom from bias.
  • Absolute error has no units: It retains the original measurement unit.
  1. [4 marks] Calculate absolute, relative and percentage error from a measurement and accepted value.
  2. [5 marks] Compare the accuracy of two measurements of different scales using percentage error.
  3. [6 marks] Evaluate a measurement process involving rounding resolution and systematic bias, recommending the most useful improvement.

Review hint: A full-mark response shows the method, keeps units and restrictions visible, interprets the result in context and checks whether the answer is reasonable.

Curriculum alignmentStart here

Every measured value is an estimate. Absolute error describes a difference in units; relative and percentage error scale that difference against the size of the quantity.

By the end of this lesson, you should be able to:

  • calculate absolute error
  • calculate relative error
  • convert relative error to percentage error
  • interpret accuracy in realistic measurement contexts
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