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LearnYPH11WPH13 · Unit 3: Practical Skills in Physics IPractical skillsReadings, uncertainties and tables
Practical skills · Subtopic 1 of 3

Readings, Uncertainties and Tables

In Paper 3 you take real measurements. Record raw readings to the precision of the instrument (a metre rule to 11 mm, a micrometer to 0.010.01 mm). Repeat readings and average them; the absolute uncertainty is about half the range. Table headings need the quantity and unit, like l / cml\,/\,\text{cm}. Calculated values get the same number of significant figures as the least precise raw data, or one more.

Cambridge 9702 Paper 3Edexcel YPH11 WPH13AQA 7408 Paper 3A≈ 35 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Record readings to the precision of the instrument.
  • Use repeat readings to estimate absolute uncertainty.
  • Calculate percentage uncertainties and combine them.
  • Set out tables with correct headings and significant figures.
Pause and think

You time 2020 swings of a pendulum as 31.431.4 s instead of timing just one swing. Why is that better?

Section 2 of 14

Core idea

Start hereYour table is your evidence

An examiner can't see you do the experiment. Your table is the only record. Units in the headings, readings to the right precision, and sensible significant figures show you measured carefully.

The big idea

Headings "quantity / unit"; raw data to instrument resolution; repeats averaged; uncertainty ≈ half the range; derived values to matching s.f.

1. Setting out

A well-set-out results table
l / cmt₁ / st₂ / sT / s20.017.9417.880.89640.025.3125.401.26860.031.0631.121.55580.035.8935.801.792
Headings show quantity and unit separated by a slash. Times for 20 swings are repeated; TT is the mean divided by 20, given to one more significant figure than the raw data at most.
  • Consistent decimal places for raw data.
  • Derived quantities: same s.f. as raw data, or one more.
  • Repeat and average; uncertainty = half the range.
Worked exampleTiming 20 swings

32.1 s, 31.8 s, 32.3 s.

Goal
Mean, uncertainty, period.
Strategy
Average; half range; ÷20.
  1. 32.1+31.8+32.33=32.07 s\frac{32.1+31.8+32.3}3=32.07\text{ s}
    Mean.
  2. 32.3−31.82=0.25 s\frac{32.3-31.8}2=0.25\text{ s}
    Half range.
  3. T=32.0720=1.60±0.01 sT=\frac{32.07}{20}=1.60\pm0.01\text{ s}
    Divide both.
AnswerT=1.60±0.01T=1.60\pm0.01 s.
✓ CheckPercentage uncertainty ~0.8% ✓.
Common misconceptionDropping zeros A metre rule reading of 34 cm should be written 34.034.0 cm.

Summary

  • Quantity / unit headings.
  • Precision matched to instrument.
Key words
Resolution
Smallest change an instrument can show.
HistoryPrecision makes discoveries. Argon was discovered in 18941894 because Lord Rayleigh noticed nitrogen from air was 0.5%0.5\% denser than nitrogen made chemically. Only a careful estimate of his uncertainties convinced him the difference was real, not error. It earned him a Nobel Prize.
Fun factThickness of a sheet of paper. A ruler can't measure a single sheet of paper (0.10.1 mm), but measure 500500 sheets in a ream (about 5.05.0 cm) and divide: 0.1000.100 mm with only 2%2\% uncertainty. Measuring many and dividing is one of the oldest tricks in experimental physics.
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