A LevelPhysicsAQARevision NotesMeasurements & Their ErrorsUse of SI Units & Their PrefixesPowers of Ten

Powers of Ten (AQA A Level Physics): Revision Note

Exam code: 7408

Written by: Katie M

Reviewed by: Timothy Sit

Updated on 14 September 2026

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Understand this topic with deeper explanations and understanding checks.

Powers of ten

Physical quantities can span a huge range of values
For example:
- the diameter of an atom is about 10^–10 m (0.0000000001 m)
- the width of a galaxy may be about 10²¹ m (1 000 000 000 000 000 000 000 m)
  - This is a difference of 31 powers of ten
Powers of ten are numbers that can be achieved by multiplying 10 times itself
It is useful to know the prefixes for certain powers of ten

Prefix	Abbreviation	Value
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

For example:
- 5 kN = 5 kilonewtons = 5 × 10³ N (5000 N)
- 7 nC = 7 nanocoulombs = 7 × 10^-9 C (0.000000007 C)

Examiner Tips and Tricks

You will often see very large or very small numbers categorised by powers of ten, so it is very important you become familiar with these as getting these prefixes wrong is a very common exam mistake.

Common unit conversions

J and eV

A common unit conversion in physics is between Joules (J) and electronvolts (eV)
The electronvolt is derived from the equation work done (or energy transferred) W = qV
- 1 eV = 1.6 × 10^–19 C × 1 V = 1.6 × 10^–19 J
To convert from J → eV, divide by 1.6 × 10^–19
To convert from eV → J, multiply by 1.6 × 10^–19

J and kW h

Another common unit conversion in physics is between Joules (J) and kilowatt-hours (kW h)
To convert between J and kW h, expand the derived units and re-collect terms as follows:
- 1 kW h = 3600 kW s (since 1 hour = 3600 s)
- 3600 kW s = 3 600 000 W s (since 1 kW = 1000 W)
- 3 600 000 W s = 3 600 000 J = 3.6 MJ (since power = energy / time or 1 W = 1 J s^–1)
To convert from J → kW h, divide by 3.6 × 10⁶
To convert from kW h → J, multiply by 3.6 × 10⁶

Worked Example

The ionisation energy of hydrogen is 2.176 × 10^–18 J. Calculate this energy in eV.

[2]

Answer:

To convert from J → eV, divide by 1.6 × 10^–19 J

$Energy in eV = \frac{2.176 \times 10^{- 18}}{1.6 \times 10^{- 19}}$ [1 mark]

$Energy in eV = 13.6 eV$ [1 mark]

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