Use of SI Units and Their Prefixes

This guide covers sub-topic 3.1.1 Use of SI units and their prefixes, the first of three sub-topics in Topic 3.1 Measurements and their errors, from the AQA A-level Physics (7408) specification (first teaching September 2015). This content is shared with the co-teachable AS Physics (7407) and is normally taught in year 1.

Before studying this

This is the opening topic of the specification. A working knowledge of SI units underpins every later topic, so it is worth mastering before moving on to Particles and radiation.

Syllabus coverage

AQA A-LEVEL PHYSICS (7408) — Sub-topic 3.1.1

Fundamental (base) units. Use of mass, length, time, amount of substance, temperature, electric current and their associated SI units. SI units derived. Knowledge and use of the SI prefixes, values and standard form. The fundamental unit of light intensity, the candela, is excluded. Students are not expected to recall definitions of the fundamental quantities. Dimensional analysis is not required.

Students should be able to use the prefixes: T, G, M, k, c, m, μ, n, p, f. Students should be able to convert between different units of the same quantity, e.g. J and eV, J and kW h.

Fundamental (base) SI units

A working knowledge of the fundamental (base) units of measurement is vital to the continuing study of physics. The specification requires familiarity with mass, length, time, amount of substance, temperature, and electric current, and their associated SI units:

• mass — kilogram (kg)
• length — metre (m)
• time — second (s)
• amount of substance — mole (mol)
• temperature — kelvin (K)
• electric current — ampere (A)

The fundamental unit of light intensity, the candela, is excluded from this specification. Students are not expected to recall formal definitions of these fundamental quantities, and dimensional analysis (checking equations by comparing base units) is not required at A-level.

Derived SI units

All other SI units are derived units, built by combining the base units through the relationships that define them. For example, speed is derived from length divided by time (m s⁻¹), and force is derived from mass × acceleration (kg m s⁻²), which is given the derived unit newton (N).

SI prefixes and standard form

Physical quantities in A-level Physics span an enormous range of magnitudes, from the size of a nucleus to the size of a galaxy, so SI prefixes and standard form are used throughout the course. Students should be able to use the following prefixes:

Prefix	Symbol	Multiplying factor
tera	T	×10¹²
giga	G	×10⁹
mega	M	×10⁶
kilo	k	×10³
centi	c	×10⁻²
milli	m	×10⁻³
micro	μ	×10⁻⁶
nano	n	×10⁻⁹
pico	p	×10⁻¹²
femto	f	×10⁻¹⁵

Converting between units of the same quantity

Students should be able to convert between different units used for the same physical quantity. Two conversions specifically named in the specification are between joules (J) and electronvolts (eV), and between joules (J) and kilowatt-hours (kW h).

Worked example – kilowatt-hours to joules. A domestic energy meter records 4.2 kW h of electrical energy used, given 1 kW h = 3.6 x 10^6 J.

energy in J = energy in kW h x 3.6 x 10^6
energy in J = 4.2 x 3.6 x 10^6 = 1.512 x 10^7 J

The kilowatt-hour is a non-SI unit still used on household energy bills precisely because a joule is an inconveniently small unit for the amount of energy a home uses in a day – converting it to joules is what puts it on the same footing as every other energy calculation in the specification.

Worked example. An electron is accelerated through a potential difference so that it gains 3.2 × 10⁻¹⁸ J of kinetic energy. Express this energy in electronvolts (1 eV = 1.6 × 10⁻¹⁹ J).

energy in eV = energy in J ÷ (1.6 × 10⁻¹⁹)
energy in eV = 3.2 × 10⁻¹⁸ ÷ 1.6 × 10⁻¹⁹ = 20 eV

Worked example – prefixed units in a calculation. A student measures a current as 250 mA and substitutes 250 directly into an equation that requires SI base units.

250 mA is NOT 250 A -- "m" here means milli, x10^-3
250 mA = 250 x 10^-3 A = 0.25 A

Substituting 250 instead of 0.25 makes the final answer wrong by a factor of 1000, even though every other step of the calculation is correct – this is one of the most common ways marks are lost on questions that otherwise test a different topic entirely, because the unit-conversion error happens right at the start.

Common mistakes

Mixing up prefixes with similar-sounding names, e.g. milli (10⁻³) and micro (10⁻⁶) — always double check the exponent, not just the letter. Forgetting to convert a quantity into base SI units before substituting into an equation (e.g. leaving a length in cm, or a current in mA, rather than converting to m or A). Confusing mass (kg) with weight (N) when reading “fundamental quantities.”

Quick revision checklist

• List the fundamental (base) quantities and their SI units: mass, length, time, amount of substance, temperature, electric current.
• Explain the difference between a base unit and a derived unit.
• Recall and use the prefixes T, G, M, k, c, m, μ, n, p, f with standard form.
• Convert between J and eV, and between J and kW h.

Related resources

• Use of SI Units and Their Prefixes practice questions
• Limitation of Physical Measurements — the next sub-topic
• AQA A Level Physics hub

This guide is intended to support, not replace, engagement with the official AQA specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.