Measurement, Units, and Laboratory Skills
Measurement, Units, and Laboratory Skills: what is tested
This domain checks SI units, prefixes, significant figures, uncertainty analysis, and graphical interpretation. The exam tests whether you can report a measurement honestly and extract a physical relationship from a graph.
Core rules
- SI base units include metre, kilogram, second, ampere, kelvin, mole, and candela. Derived units combine them; for example, 1 N = 1 kg·m·s⁻² and 1 J = 1 N·m.
- Prefixes scale by powers of ten: nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, kilo 10³, mega 10⁶.
- In multiplication and division, keep the least number of significant figures in the data. In addition and subtraction, keep the least number of decimal places.
- Absolute uncertainty has the same unit as the quantity. Relative uncertainty is absolute uncertainty divided by the value; percentage uncertainty is relative uncertainty × 100%.
- When adding or subtracting, add absolute uncertainties. When multiplying or dividing, add percentage uncertainties.
- On a graph, the gradient of a straight-line fit is Δy/Δx and carries units from both axes. The intercept may represent a systematic offset. Error bars show uncertainty, not the range of all data.
Worked example
A block has mass m = 24.0 ± 0.2 g and volume V = 8.0 ± 0.2 cm³. Density is ρ = m/V = 3.0 g/cm³. The percentage uncertainties are 0.2/24.0 = 0.83% and 0.2/8.0 = 2.5%, giving 3.3% in total. The absolute uncertainty is 0.033 × 3.0 ≈ 0.1 g/cm³, so the result is 3.0 ± 0.1 g/cm³. Reporting 3.00 g/cm³ would overstate precision.
Traps that cost marks
Do not mix units before calculating; convert mm to m and g to kg. Precision is not accuracy: repeated readings may be precise but systematically offset by a zero error. A line of best fit is not a join-the-dots exercise. Read the gradient using points on the fitted line, not raw data points. Keep uncertainty to one significant figure in most reports, and do not quote more significant figures than the apparatus justifies.