2. Resolution Limitation
2.1. Examples
A ruler marked in millimetres cannot reliably measure a length of 3.4 mm — the true value must be estimated between the 3 mm and 4 mm graduations, introducing uncertainty
A stopwatch reading to 0.1 s cannot distinguish between reaction times of 1.21 s and 1.24 s — both would be recorded as 1.2 s
A thermometer graduated in 1 °C divisions cannot reliably record a temperature of 36.6 °C — the observer must estimate between 36 °C and 37 °C
A balance reading to 0.1 g cannot detect a mass difference of 0.04 g between two samples
A measuring cylinder graduated in 2 mL divisions requires estimation for any volume that falls between graduations, introducing uncertainty in every reading
Resolution Limitation: A Four-Step Analysis
Use the four-step framework to analyse a resolution limitation:
- Step 1 — Identify the source
Instrumental — the scale divisions of the measuring instrument are too coarse to capture the precision required by the investigation.
- Step 2 — Classify the behaviour
Unpredictable spread → Random error → affects precision. The amount and direction of the estimation error varies between readings, producing a spread of results around the true value.
- Step 3 — Explain the impact
Each reading carries an inherent uncertainty of at least half the smallest scale division. Because the estimation varies between trials, results are scattered around the true value rather than consistently displaced in one direction. Accuracy is not affected — the readings are centred on the true value — but precision is reduced.
- Step 4 — Suggest an improvement
Resolution limitation is reduced by using an instrument with smaller scale divisions — it cannot be eliminated by repeating measurements alone, though averaging multiple readings will reduce its effect.
2.2. Effects
Resolution limitation produces random scatter around the true value. Because the estimation between graduations varies unpredictably:
results are scattered above and below the true value rather than consistently displaced in one direction,
precision is reduced — repeated readings may not agree closely with each other,
accuracy is not affected — there is no consistent bias; readings are centred on the true value on average,
the minimum uncertainty introduced is half the smallest scale division — for example, a ruler marked in 1 mm divisions introduces an uncertainty of at least ±0.5 mm per reading,
repeating measurements and averaging will reduce the effect, but the limitation remains unless a higher-resolution instrument is used.
2.3. Improvements
To reduce resolution limitation, use an instrument with a finer scale or a higher-resolution sensor.
Replace the instrument with one that has smaller scale divisions — for example, use a digital calliper (0.01 mm resolution) instead of a ruler (1 mm resolution).
Use a digital instrument rather than an analogue one where possible, as digital displays typically offer greater resolution.
Repeat measurements and calculate a mean to reduce the effect of random estimation error across trials.
Report all measurements to the correct number of significant figures consistent with the instrument’s resolution — do not record more decimal places than the instrument can support.
When designing the investigation, select instruments whose resolution is appropriate for the precision required — consider the magnitude of the quantity being measured and the differences expected between conditions.
Structured Question: Resolution Limitation
A Year 8 class is investigating whether the width of a rubber band affects how far it stretches when a 100 g mass is hung from it. Each student measures the length of the rubber band before and after the mass is added, then calculates the extension by subtracting the original length. The students use a ruler marked in centimetres only, with no millimetre graduations. Several students notice that the end of the rubber band often falls between two centimetre marks, and each student estimates the position slightly differently.
(a) Identify the type of error introduced by using a ruler with centimetre-only graduations and classify it as random, systematic, or personal. (2 marks)
(b) Explain how this error would affect the group’s extension 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 five times and calculates a mean extension. 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 reduce this error before collecting data. (1 mark)
Reveal Answer Key
(a)
The error is a resolution limitation, classified as a random error.
(1 mark for naming resolution limitation; 1 mark for random)
(b)
Because the ruler has centimetre-only graduations, the true length of the rubber band often falls between two marks and must be estimated. Each student estimates this differently — sometimes rounding up, sometimes rounding down — so the recorded values are scattered unpredictably above and below the true length. There is no consistent direction to the error. (1 mark)
The precision of the results is reduced — repeated measurements of the same extension will not always agree, as each reading involves a different estimate between the centimetre marks. The minimum uncertainty introduced is at least ±0.5 cm per reading, and since the extension is calculated by subtracting two measurements, this uncertainty accumulates across both readings. (1 mark)
The accuracy is not systematically affected — because estimates are sometimes too high and sometimes too low, the errors tend to cancel out over many measurements and the mean is likely to be close to the true extension. (1 mark)
(c)
Repeating each measurement five times and averaging would help reduce the effect of this error, although it cannot eliminate it entirely. (1 mark)
Because the estimation error varies unpredictably — sometimes above, sometimes below the true value — averaging across multiple readings allows these opposing errors to partially cancel out, bringing the mean closer to the true extension. However, the resolution limitation remains as long as the same ruler is used; increasing the number of trials further would reduce but never fully eliminate the effect. (1 mark)
(d)
The group should replace the centimetre-only ruler with one that has millimetre graduations, reducing the minimum uncertainty from ±0.5 cm to ±0.5 mm per reading and allowing the extension to be measured with greater precision. (1 mark)
Part (a): accept “resolution limitation” or “the instrument’s scale divisions are too coarse to measure the quantity precisely.” Do not accept “parallax error” — the stem does not describe an incorrect viewing angle. Do not accept “operator error” or “recording error” — estimating between graduations is an inherent limitation of the instrument, not a one-off mistake by the student.
Part (b): award the direction mark for a response that correctly identifies there is no consistent direction — estimates are scattered both above and below the true value. Do not award this mark for a response that states results are consistently too high or too low. Award the precision mark for correctly stating precision is reduced and linking this to the uncertainty in estimating between graduations. A stronger response may note that the uncertainty accumulates across both the before and after measurements. Award the accuracy mark for correctly stating accuracy is not systematically affected because estimation errors tend to cancel out across trials.
Part (c): repeating and averaging does help for random errors. Award both marks only if the student correctly identifies that averaging helps and explains why: opposing estimation errors partially cancel out. A response that states repeating always reduces error without this reasoning should receive only 1 mark. A response that correctly notes the limitation remains unless a better instrument is used may receive full marks if the averaging reasoning is also present.
Part (d): accept “use a digital calliper” or “use a ruler with millimetre graduations” as valid responses. Do not accept “repeat measurements” as this has already been addressed in part (c) and only reduces rather than eliminates the error. Do not accept “be more careful when reading” — the limitation is in the instrument’s scale, not the student’s attention.