Absolute, Relative and Percentage Measurement Error — AC9M9M04

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

Recall rounding, percentages, absolute value, units and calculator division. Understand that measured values have finite precision.

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.

• 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. A mass is measured as 248 g instead of 250 g. Find absolute and percentage error.
2. Compare a 2 mm error on 40 mm with a 2 mm error on 2 m.
3. State the rounding interval for 7.3 m measured to the nearest 0.1 m.

Guided method: Name the mathematical structure first, show the calculation or representation, then verify with an estimate, inverse operation, second representation or digital check.

1. Find absolute error when 19.6 cm is measured against 20.0 cm.
2. Find relative and percentage error for that measurement.
3. Which is more accurate: 99 g for 100 g or 995 g for 1000 g?
4. A thermometer has a constant +0.6°C bias. Explain why repeated readings do not remove it.
5. Give bounds for 450 m rounded to the nearest 10 m.
6. Explain accuracy versus precision with an example.

Two instruments give measurements with smaller spread from one another, but one has a known calibration bias. Decide which is more precise and which may be more accurate, explaining why the judgements can differ.

Reasoning standard: Make a claim, show the relevant mathematical evidence, explain why it supports the conclusion and state any condition or limitation.

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.

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.

• I can distinguish absolute and relative error.
• I can calculate percentage error correctly.
• I can interpret rounding intervals.
• I can compare errors across different scales.
• I can distinguish precision from accuracy.

Exit ticket: Solve one unfamiliar example and explain the key decision in words, not just symbols.

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.

Use these links to move through the Year 9 learning sequence rather than studying the code in isolation.

• AC9M9M02 — Scientific Notation for Very Large and Very Small Measurements
• AC9M9M05 — Direct Proportion, Rates, Ratio and Scale Modelling

• Australian Curriculum v9.0 — Mathematics
• Victorian Curriculum F–10 Version 2.0 — Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for Calculate and interpret absolute, relative and percentage errors in measurements...

Mapped skill: calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.