Measurement and Units
Measurement and Units is the toolkit domain: the exam checks that you can choose and use SI units, convert prefixes confidently, read instruments to the correct precision, and handle density and uncertainty without losing marks.
Core rules and concepts
- SI base units: length metre (m), mass kilogram (kg), time second (s), electric current ampere (A), thermodynamic temperature kelvin (K), amount mole (mol), luminous intensity candela (cd).
- Prefixes: nano 10^-9, micro 10^-6, milli 10^-3, centi 10^-2, kilo 10^3, mega 10^6, giga 10^9. Convert by multiplying by the power of ten; check direction when changing a small unit into a large one.
- Derived units: speed m/s, force N = kg m/s², pressure Pa = N/m², energy J = N m, power W = J/s, density kg/m³.
- Density ρ = m/V. For an irregular solid use displacement; for a liquid subtract the initial cylinder reading.
- Uncertainty: an analogue scale is usually ± half the smallest division; a digital display is ± the last digit. Repeat readings and average; subtract any zero error.
- Give final answers to sensible significant figures, usually 2 or 3 s.f., matching the least precise measurement.
Worked example
Convert 2.5 g/cm³ to kg/m³ and find the mass of 200 cm³. 1 g/cm³ = 1000 kg/m³, so 2.5 g/cm³ = 2.5 × 1000 = 2500 kg/m³. 200 cm³ = 200 × 10^-6 m³ = 2.0 × 10^-4 m³. m = ρV = 2500 × 2.0 × 10^-4 = 0.50 kg. Reasoning: convert volume first; mixing cm³ with kg/m³ is the commonest error.
Traps that cost marks
- 1 cm³ = 10^-6 m³, not 10^-2 m³.
- Prefix direction: 5 mA = 5 × 10^-3 A, not 5 × 10^3 A.
- Reading a vernier or micrometer without subtracting zero error.
- Quoting every calculator digit instead of a sensible significant-figure answer.
- Confusing mass in kg with weight in N.