Measurements, Units, Errors and Practical Skills
What this domain tests
Measurements questions check that you can choose units, quote a result with honest uncertainty and describe a practical procedure precisely. A/L papers rarely ask for definitions alone; they embed these skills in density, resistivity or Young modulus experiments.
Core rules
- SI base units are kg, m, s, A, K, mol and cd. Check homogeneity by reducing both sides to base units.
- Prefixes run from pico (10^-12) to tera (10^12). Convert to SI before calculating.
- Random errors scatter readings and shrink when you average repeats; systematic errors shift every reading, for example a zero error or calibration offset.
- For Q = k a^m b^n, percentage uncertainties add after weighting: %Q = m%a + n%b.
- A micrometer (0.01 mm resolution) suits small diameters; vernier calipers suit lengths. Record to the resolution and estimate the final digit.
Worked example
A cylinder has mass 84.0 ± 0.4 g, diameter 20.00 ± 0.05 mm and length 50.0 ± 0.5 mm. Density ρ = 4m/(πd²l). Percentage uncertainties: mass 0.48%, diameter 0.25% but doubled to 0.50%, length 1.0%. Total ≈ 2.0%. The mean density is 5.35 g cm^-3, so quote (5.35 ± 0.11) g cm^-3. The length dominates, so a better balance would barely help.
Traps
Mixing mm and m; quoting too many significant figures; treating a zero error as random; saying repeats remove systematic error; forgetting to double the diameter uncertainty because d is squared.