Experimental data & uncertainty · SL/HL
Uncertainty propagation
Combine uncertainties using school-lab rules.
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Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Measured quantities. | |
| Absolute uncertainties. |
Worked example
- Operation
- Division a / b
- Value a
- 25.00
- Absolute uncertainty in a
- 0.05
- Value b
- 24.60
- Absolute uncertainty in b
- 0.05
- Result unit (optional)
- Uncertainty significant figures
- 1 significant figure
(1.016 ± 0.004)
Follow the example steps
- z = 25 ÷ 24.6 = 1.01626
- pₐ = 0.2%; pᵦ = 0.203252%
- p_z ≈ pₐ + pᵦ = 0.403252%
- Δz ≈ |z|p_z/100 = 0.00409809
- Rounded result: (1.016 ± 0.004)
Common mistakes
Absolute uncertainties add for a difference.
Incorrect approach
(10 ± 0.2) − (4 ± 0.1): Δz = 0.2 − 0.1
Correct approach
z = 6; Δz = 0.2 + 0.1 = 0.3
More checks before you submit
- Absolute uncertainties add even when measured values are subtracted.
- Power propagation is HL-only in the current Chemistry guide.
Method notes
These are the linear propagation rules specified for course data processing. They are not a replacement for a full statistical uncertainty model.