2. Zero Error
2.1. Examples
A top-pan balance displaying 0.3 g before any sample is placed on it, so every mass reading is 0.3 g too high
A spring scale reading 2 N with no load applied, so all force measurements are 2 N above the true value
A thermometer reading 1 °C in an ice-water bath that should be 0 °C, so all temperature readings are 1 °C too high
A burette that has a bubble in the tip, so the initial volume reading is incorrect and all volume measurements are affected
A pH meter not calibrated to pH 7 before use, causing all readings to be offset by a consistent amount
Zero Error: A Four-Step Analysis
Use the four-step framework to analyse zero error:
- Step 1 — Identify the source
Instrumental — the measuring device has a built-in offset that is present before any measurement is taken.
- Step 2 — Classify the behaviour
Consistent, one-direction shift → Systematic error → affects accuracy. Every reading is shifted by the same amount in the same direction.
- Step 3 — Explain the impact
All results are shifted too high or too low by the same amount. The error cannot be detected by repeating measurements, as every repeat is affected equally. Precision is unaffected — results will agree with each other — but none will be close to the true value.
- Step 4 — Suggest an improvement
Zero errors are eliminated, not averaged out — check and correct the instrument before taking any measurements.
2.2. Effects
Zero error produces a consistent offset across all measurements. Because every reading is shifted by the same amount in the same direction:
results will appear precise (repeats agree with each other),
but accuracy is reduced — all values are displaced from the true value,
repeating measurements does not help, as the error affects every reading equally,
the offset can sometimes be corrected mathematically if the zero error value is known and stable.
2.3. Improvements
To eliminate zero error, check and zero the instrument before use and verify it is within calibration.
Check that the instrument reads zero before any measurement is taken; adjust using the zero-adjustment screw or tare function if available.
If the zero error is known and constant, subtract it from all readings as a correction factor.
Re-zero the instrument between trials if it is prone to drift.
Have the instrument professionally calibrated or replaced if the zero error cannot be reliably corrected.
Structured Question: Zero Error
A Year 8 class is investigating how the mass of a paper cup changes when different volumes of water are added to it. Before beginning, the teacher instructs students to place the empty cup on the balance and record the starting mass. One group notices their balance displays 0.4 g before they place anything on it. They do not adjust the balance and proceed to record all their measurements.
(a) Identify the type of error present in this investigation and classify it as random, systematic, or personal. (2 marks)
(b) Explain how this error would affect the group’s mass measurements. In your answer, refer to the direction of the error and its effect on the accuracy and precision of the results. (3 marks)
(c) The group repeats each measurement three times and calculates a mean. Evaluate whether this would reduce the effect of the error identified in part (a). (2 marks)
(d) Describe one improvement the group could make to eliminate this error before collecting data. (1 mark)
Reveal Answer Key
(a)
The error is a zero error, classified as a systematic error.
(1 mark for naming zero error; 1 mark for systematic)
(b)
Because the balance displays 0.4 g before anything is placed on it, every mass reading includes an extra 0.4 g that is not part of the cup or water. This means all measurements will be consistently overestimated by 0.4 g — every reading is displaced in the same direction by the same amount. (1 mark)
The accuracy of the results is reduced, as all recorded masses are 0.4 g higher than the true mass. (1 mark)
The precision is unaffected — because the same offset is present in every reading, the repeated measurements will agree closely with each other. (1 mark)
(c)
Repeating measurements and calculating a mean would not reduce the effect of this error. (1 mark)
Because the balance displays 0.4 g before every reading, each repeat includes the same offset in the same direction. Averaging does not cancel a consistent offset — it only reduces the effect of random errors, which vary unpredictably between trials. (1 mark)
(d)
The group should use the tare or zero function on the balance to set the display to 0.0 g before placing the cup on it, or select a different balance that reads zero when empty. (1 mark)
Part (a): accept “zero error” or “the balance has not been zeroed.” Do not accept “human error” or “mistake” — the balance itself has a fault, so this is an instrumental error, not a personal error.
Part (b): award the direction mark only if the student identifies overestimation specifically, not just “the results are wrong.” Award the precision mark only if the student correctly states precision is unaffected and provides a reason. A response that states precision is also reduced should not receive the precision mark.
Part (c): a response that simply states “repeating reduces error” without explaining why it does not apply here should not receive full marks. The key reasoning is that the offset is identical in every trial.
Part (d): accept “subtract 0.4 g from all readings as a correction factor” as an alternative valid response, since the offset is known and constant.