Measurement, Units and the Scientific Method
Measurement, units and the scientific method is examined through practical-style calculations rather than recall: you must choose an instrument, record a value with its uncertainty, and justify a conclusion from data. Expect SI units, prefixes, dimensional consistency, significant figures and graph work.
SI units and prefixes
The seven base units are metre, kilogram, second, ampere, kelvin, mole and candela. Derived units are combinations: N = kg m s⁻², J = N m, Pa = N m⁻², W = J s⁻¹, C = A s, V = W A⁻¹. Prefixes change the power of ten only: nano 10⁻⁹, micro 10⁻⁶, milli 10⁻³, kilo 10³, mega 10⁶, giga 10⁹.
Dimensions
Write [F] = M L T⁻² and [pressure] = M L⁻¹ T⁻². An equation is valid only if both sides have the same dimensions; this catches errors such as adding a force to an energy.
Uncertainty and significant figures
For a single reading, the uncertainty is at least half the smallest division, plus any zero error. When adding or subtracting, add absolute uncertainties; when multiplying or dividing, add percentage uncertainties. Quote a final answer to the same number of significant figures as the least precise input.
Planning and graphs
Identify independent, dependent and controlled variables, repeat readings, and plot the dependent variable on the y-axis. The gradient carries units taken from the axes.
Worked example
A cylinder has m = 25.40 ± 0.05 g, d = 1.20 ± 0.01 cm and h = 5.00 ± 0.05 cm. V = πd²h/4 = π(1.20)²(5.00)/4 = 5.655 cm³. Density = 25.40/5.655 = 4.49 g cm⁻³. Percentage uncertainty = (0.05/25.40) + 2(0.01/1.20) + (0.05/5.00) = 0.20% + 1.67% + 1.00% = 2.87%, so ±0.13 g cm⁻³. Report (4.49 ± 0.13) g cm⁻³.
Traps
Using diameter as radius, mixing mm and m, over-rounding intermediate values, and ignoring zero error on vernier calipers.