A student measures the length of a short metal rod using a ruler and records a single measurement of 8 mm. Explain why this method produces a result with a high percentage uncertainty, and state one change the student could make to reduce this percentage uncertainty.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
A small measurement has a high percentage uncertainty because the uncertainty is a large fraction of the measured value.
The absolute uncertainty of a ruler reading is fixed (e.g. ±0.5 mm or ±1 mm). When the measured value is only 8 mm, this fixed uncertainty represents a large proportion of the value, giving a high percentage uncertainty.
The student could use a micrometer screw gauge instead of a ruler.
A micrometer measures to 0.01 mm, so the absolute uncertainty is much smaller relative to the measurement, giving a lower percentage uncertainty.
The absolute uncertainty of a ruler reading is fixed (e.g. ±0.5 mm or ±1 mm). When the measured value is only 8 mm, this fixed uncertainty represents a large proportion of the value, giving a high percentage uncertainty.
The student could use a micrometer screw gauge instead of a ruler.
A micrometer measures to 0.01 mm, so the absolute uncertainty is much smaller relative to the measurement, giving a lower percentage uncertainty.
Examiner tips
- Show the relationship between absolute and percentage uncertainty; use the formula %U = (Δx/x)×100. Mention the fixed ±0.5 mm (or ±1 mm) uncertainty of a ruler. State the alternative tool (micrometer) and its higher precision (0.01 mm).
Common mistakes
- Assuming the ruler has zero uncertainty or ignoring the fixed ±0.5 mm. Failing to explain that the percentage uncertainty is calculated from the ratio of absolute to measured value. Not naming a specific instrument that reduces uncertainty, e.g. a micrometer screw gauge.
Mark scheme (4 marks)
- A small measurement has a high percentage uncertainty because the uncertainty is a large fraction / proportion of the measured value
- The absolute uncertainty of a ruler reading is fixed (e.g. ±0.5 mm or ±1 mm), so when the measured value is small, the percentage uncertainty is large
- Use a micrometer screw gauge instead of a ruler to measure the rod
- A micrometer screw gauge measures to 0.01 mm, so the absolute uncertainty is much smaller relative to the measurement, giving a lower percentage uncertainty
Key terms in this question
Related
- All Cambridge International IGCSE Physics (0625) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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