Measurement, Units, and Data Analysis
This domain tests fluency with SI units and prefixes, unit conversion, significant figures, uncertainty, and the interpretation of tables and graphs. Expect items that ask you to convert a quantity, report an answer to the correct number of significant figures, compute a derived quantity such as density, or read a gradient with its units.
Base units, prefixes and derived units
- SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
- Prefixes: nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, centi 10⁻², kilo 10³, mega 10⁶, giga 10⁹.
- Derived equivalences: 1 N = 1 kg·m/s²; 1 J = 1 N·m; 1 W = 1 J/s; 1 Pa = 1 N/m²; 1 V = 1 J/C; 1 Ω = 1 V/A.
- 1 mL = 1 cm³; 1 cm² = 10⁻⁴ m²; 1 cm³ = 10⁻⁶ m³.
Significant figures and uncertainty
Multiplication and division keep the smallest number of significant figures in the inputs; addition and subtraction keep the smallest number of decimal places. Leading zeros are never significant, sandwich zeros always are, and trailing zeros count only after a decimal point. Percent error = |measured − accepted| ÷ accepted × 100.
Worked example
A rectangular block measures 2.0 cm × 3.0 cm × 5.0 cm and has a mass of 240 g. Find its density in kg/m³.
Volume = 2.0 × 3.0 × 5.0 = 30 cm³ (two significant figures, limited by the 2.0 cm measurement). Density = 240 g ÷ 30 cm³ = 8.0 g/cm³. Convert: 8.0 g/cm³ × (10⁻³ kg/g) ÷ (10⁻⁶ m³/cm³) = 8.0 × 10³ kg/m³. The answer carries two significant figures because the volume and the 2.0 cm side both do.
Traps that cost marks
- Converting cm² or cm³ with a single factor of 100 instead of 10⁴ or 10⁶.
- Reporting a calculator's full string of digits rather than the significant-figure answer.
- Confusing precision (repeatability) with accuracy (closeness to the true value).
- Plotting the dependent variable on the x-axis; slope units come from y-units divided by x-units.
- Averaging in an obvious outlier without comment, or quoting a mean for skewed data instead of the median.