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S1.3.3—Units and numerical values

Syllabus
First assessment 2025
Objective
S1.3.3
Level
HL

Control Units and Figures

Make every number carry a compatible unit

Convert prefixes before substitution and use the symbols defined in the guide/data booklet. The SI base units most often used in physics are metre (m), kilogram (kg), second (s), ampere (A) and kelvin (K); mole (mol) and candela (cd) complete the SI base set.

Prefix Symbol Factor Example
giga G 10910^9 2.0 GHz=2.0×109 Hz2.0\,\text{GHz}=2.0\times10^9\,\text{Hz}
kilo k 10310^3 3.0 km=3.0×103 m3.0\,\text{km}=3.0\times10^3\,\text{m}
milli m 10−310^{-3} 3.2 mA=3.2×10−3 A3.2\,\text{mA}=3.2\times10^{-3}\,\text{A}
micro μ\mu 10−610^{-6} 5.0 μs=5.0×10−6 s5.0\,\mu\text{s}=5.0\times10^{-6}\,\text{s}
nano n 10−910^{-9} 450 nm=4.50×10−7 m450\,\text{nm}=4.50\times10^{-7}\,\text{m}

Use units as an equation check

For E=12mv2E=\tfrac12mv^2, the right side has units kg m2 s−2=J\text{kg}\,\text{m}^2\,\text{s}^{-2}=\text{J}, so it can represent energy. This unit check can reject an expression, but matching units alone do not prove that its numerical factor or physics is correct.

Round once, at the end

Keep guard digits during working. Report the final value and its uncertainty to compatible decimal places, with the uncertainty usually at one significant figure (or two when needed to avoid misleading rounding). Units such as eV, ly, pc, hour, day and year may be used where the syllabus context makes them appropriate.

S1.3.3 Exam Analysis

Assessment in practice

1–2 marks
How it is assessed

Questions compare distances written with different prefixes or report a measured quantity with absolute uncertainty.

Command terms

Identify / Write

What earns marks

Convert prefixes before comparison and round the final value and uncertainty appropriately.

Watch for

Comparing exponent values without converting prefixes or retaining unjustified significant figures.

Retrieve Mathematical Practice

Calculate carefully

Rearrange symbolically, resolve vectors, convert units and use proportional reasoning before substituting.

Report evidence

Propagate uncertainty with the correct operation, then use labelled graphs, error bars, gradients, intercepts and areas to test the model.