A number without a unit is not an answer. Get the units right, use the prefixes properly, and quote a sensible number of digits — and you will stop losing marks you have already earned.
📚 What you need to know
There are 7 SI base units. Everything else is derived from them.
The four that matter most in chemistry: kilogram, second, kelvin, mole.
Prefixes are powers of ten: kilo is 103, milli is 10–3, and so on.
The full prefix list is in Section 3 of the data booklet.
The same letter can mean several things — context decides.
Significant figures: all non-zero digits count; so do zeros between them.
Leading zeros never count. Trailing zeros count only if there is a decimal point.
Your final answer should have no more significant figures than the least precise measurement you used.
The SI base units
Seven units, defined independently, from which every other unit in science is built.
Quantity
SI base unit
Symbol
length
metre
m
mass
kilogram
kg
time
second
s
temperature
kelvin
K
amount of substance
mole
mol
electric current
ampere
A
luminous intensity
candela
cd
Notice that the base unit of mass is the kilogram, not the gram. It is the only base unit that already has a prefix built into its name, which is a historical quirk rather than anything meaningful.
Units you will actually use
Quantity
Unit
Symbol
energy
joule
J
pressure
pascal
Pa
electric charge
coulomb
C
enthalpy change
kilojoules per mole
kJ mol–1
entropy
joules per kelvin per mole
J K–1 mol–1
potential difference
volt
V
concentration
moles per cubic decimetre
mol dm–3
molar mass
grams per mole
g mol–1
Prefixes
Chemistry deals with atoms 10–10 m across and with 6.02 × 1023 particles in a mole. Prefixes exist so you do not have to write all those zeros out.
Converting is always the same move: replace the prefix with its power of ten, then tidy into standard form.
Prefix
Symbol
Power of ten
Example
mega-
M
106
4.2 MJ = 4.2 × 106 J
kilo-
k
103
5.2 kg = 5200 g
centi-
c
10–2
1 dm3 = 1000 cm3
milli-
m
10–3
25 cm3 = 0.025 dm3
micro-
µ
10–6
1 µg = 10–6 g
nano-
n
10–9
1 nm = 10–9 m
pico-
p
10–12
184 pm = 1.84 × 10–10 m
🧩 Converting a unit with a prefix
Write the number without the prefix, replacing it with its power of ten. 184 pm becomes 184 × 10–12 m.
Tidy into standard form so that the first part is between 1 and 10. That gives 1.84 × 10–10 m.
Check the direction. Going to a smaller unit makes the number bigger, and vice versa.
Watch cubed units. 1 dm = 10 cm, but 1 dm3 = 1000 cm3, because the factor is cubed too.
Symbols — and why context matters
Chemistry runs out of letters very quickly. The same character means different things in different equations, so you have to read it in context.
Capitalisation is not decoration. A lower case c and a capital C are different symbols with different meanings.
Other symbol families worth keeping straight:
State symbols: (s), (l), (g), (aq). Missing these is a routine way to lose an equation mark.
Chemical symbols: from the periodic table, Section 7 of the data booklet.
Physical constants: Section 2. Planck’s constant h, the gas constant R, Avogadro’s constant L.
Terms in equations: Section 1. In n = cV, n is moles, c is concentration and V is volume.
Abbreviations: STP for standard temperature and pressure, for example.
Significant figures
Significant figures are the digits in a number that carry real information about how precisely it was measured. There are four rules and they never change.
The awkward case is 57 000. Written like that it reads as 2 s.f., which is why writing it as 5.70 × 104 is better if you really did measure three digits.
Rounding
Identify the significant figures using the rules above.
Count across to the number of figures you need.
Look at the next digit — the “rounder decider”.
If it is 5 or more, round the previous digit up. Otherwise leave it.
How many figures should you give?
The rule of thumb: your answer cannot be more precise than the least precise measurement that went into it.
Keep the full calculator value all the way through, and round only at the very end.
Never round to 1 significant figure mid-calculation. It introduces errors that can lose marks on their own.
Defined constants are different. Avogadro’s constant is quoted as 6.02 × 1023 mol–1, so use 3 s.f. for it because that is how it is defined, not because of measurement precision.
Worked examples
WORKED EXAMPLE
Calculate the number of moles in 35.75 cm3 of 0.015 mol dm–3 hydrochloric acid. Give your answer to an appropriate number of significant figures.
Convert the volume first
Concentration is per dm3, so the volume must be too.
35.75 ÷ 1000 = 0.03575 dm3Use n = cVn = 0.015 × 0.03575 = 5.3625 × 10–4Decide the significant figures
The volume has 4 s.f., the concentration has only 2 s.f., so 2 is the limit.
n = 5.4 × 10–4 molthe weakest measurement always sets the ceiling
WORKED EXAMPLE
The diameter of an aluminium atom is 184 pm. Express this in metres in standard form, and state the number of significant figures.
Replace the prefix
Pico means 10–12.
184 pm = 184 × 10–12 mTidy into standard form
The first part must be between 1 and 10, so move the point two places left and add 2 to the power.
= 1.84 × 10–10 m1.84 × 10–10 m, to 3 s.f.the power of ten changed but the significant figures did not — that is the point of standard form
💡 Exam tip
Put a unit on every answer. A bare number is usually worth nothing.
Watch out for questions that ask for “an appropriate number of significant figures” — that means you decide, from the data given.
Use the data booklet for constants and prefixes, but learn the common units by heart.
For cubed units, remember the conversion factor is cubed as well.
Include state symbols in equations unless told otherwise.
Write large or small numbers in standard form. It removes any argument about trailing zeros.
⚠️ Common mix-up
Thinking the gram is the SI base unit of mass. It is the kilogram.
Dividing by 100 to convert cm3 to dm3. It is 1000, because the length factor of 10 is cubed.
Counting leading zeros as significant. 0.00079 has two significant figures, not five.
Rounding mid-calculation. Keep everything on the calculator until the last line.
Confusing kelvin and degrees Celsius. The base unit is kelvin, and there is no degree symbol on it.
Reading a symbol out of context. The c in Q = mcΔT is not the c in n = cV.
Up next: Working with Uncertainties — where those significant figures actually come from, and what to do when uncertainties have to be combined.
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