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Apparatus readings · practical evaluation
Measurement uncertainty
Convert a supplied absolute uncertainty into a percentage and combine uncertainties for the difference between two readings.
Method and worked examples ↓Learn the method
How to approach these questions
- Read the uncertainty stated in the question; do not assume every instrument has the same uncertainty.
- Use the measured value, or the measured difference, as the denominator.
- For two readings each uncertain by ±u, the worst-case uncertainty in their difference is ±2u.
- A small measured difference can have a large percentage uncertainty even when each reading is precise.
Worked examples
A balance reading is 2.50 g. The stated absolute uncertainty is ±0.01 g. Calculate percentage uncertainty.
Percentage uncertainty = 0.01 ÷ 2.50 × 100 = 0.40%. This uses the supplied uncertainty; the display resolution alone does not establish every source of uncertainty.
A burette reads 12.0 cm³ before and 22.0 cm³ after delivery. Each reading has stated uncertainty ±0.1 cm³. Calculate worst-case percentage uncertainty in the delivered volume.
Delivered volume = 22.0 − 12.0 = 10.0 cm³. For a worst-case difference, add the absolute uncertainties: 0.1 + 0.1 = 0.2 cm³. Percentage uncertainty = 0.2 ÷ 10.0 × 100 = 2%. This is a worst-case bound, not a standard deviation.
A stem segment is measured as 18 mm on a ruler marked every 1 mm. For this question, take each endpoint reading to have uncertainty ±0.5 mm. Both endpoints are read separately. Find the worst-case uncertainty in length and its percentage.
Length is the difference between two readings. Worst-case uncertainty = 0.5 + 0.5 = ±1 mm. Percentage uncertainty = 1 ÷ 18 × 100 = 5.56%, or about 6% to one significant figure. The half-division convention is supplied for this question; it is not a universal rule for every instrument.
Keep practising
Topic map and study list · Practical data guides · Active recall decks
Course resources
AQA A-level Biology · OCR A A-level Biology · Textbook answers
Skill coverage follows the common A-level science subject content. Check your board’s current requirements: AQA 7402 and OCR A H420.