IB Biology HLSkill Set 3 — Maths for BiologyPaper 1, 2 & IACore skill~11 min read
Units, Symbols & Values
A number on its own means nothing in Biology. “The cell was 30” is not an answer. Units are the cheapest marks on the paper and the ones students throw away most often, usually by mixing up millimetres and micrometres halfway through a magnification question.
📚 What you need to know
The SI system (the metric system) is the international standard. Its base units are the metre, kilogram, second, kelvin, mole, ampere and candela.
The prefixes you need are kilo (103), centi (10−2), milli (10−3), micro (10−6) and nano (10−9).
1 cm3 is the same as 1 mL, and 1 dm3 is the same as 1 litre (= 1000 cm3).
Use the correct symbol with the unit, including index form for volumes and rates (m3, cm3 s−1).
“Amount” has a specific meaning in science — moles. Say mass, volume or concentration if that is what you mean.
Significant figures are the digits that are reliable and necessary. There are clear rules for which zeros count.
When rounding, look at the next digit along: 5 or more rounds up.
The SI base units
Everything else in science is built from these seven. You will use the first five constantly.
Quantity
SI base unit
Symbol
Where you meet it
Length
metre
m
Cell size, root growth, quadrat sides
Mass
kilogram
kg
Biomass, dry mass of a plant
Time
second
s
Every rate you ever calculate
Temperature
kelvin
K
Enzyme experiments (usually reported in °C)
Amount of substance
mole
mol
Concentration of a solution
Electric current
ampere
A
Equipment such as a data logger
Luminous intensity
candela
cd
Light intensity in photosynthesis work
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 it. Nothing breaks because of this, but it surprises people, so it is worth knowing.
Prefixes and powers of ten
Biology deals with things far too small and far too big to write out in metres. A prefix is just a shorthand for a power of ten stuck onto the front of a unit.
Prefix
Symbol
Power of ten
Example
kilo-
k
103
1 km of hedgerow in a transect
centi-
c
10−2
A 1 cm3 sample of solution
milli-
m
10−3
A leaf 40 mm across
micro-
µ
10−6
A cheek cell about 60 µm wide
nano-
n
10−9
A ribosome about 20 nm across
Going right, multiply by 1000. Going left, divide by 1000. Centimetres are the odd one out — they sit between millimetres and metres, a factor of ten and a hundred away.
🧩 Converting a unit without panicking
Write down what you have, with its unit. For example 0.45 mm.
Decide which way you are going along the ladder. Going to a smaller unit means the number gets bigger.
Count the steps. mm to µm is one step of 1000.
Multiply or divide, then write the new unit straight away: 0.45 × 1000 = 450 µm.
Check it feels right. Micrometres are tiny, so you should need more of them. 450 is bigger than 0.45. Good.
Volume, area and the units that trip people up
Volume units cause more confusion than anything else on this page, mostly because the same volume has three different names.
Concentrations in Biology are usually given per dm3, but you measure out the solution in cm3. Knowing that 1000 cm3 makes 1 dm3 saves you every time.
Measurement
Base unit
Conversions worth memorising
Length
metre (m)
1000 m = 1 km; 100 cm = 1 m; 1000 mm = 1 m; 1 000 000 µm = 1 m
Volume
cubic metre (m3)
1000 cm3 = 1 dm3; 1 cm3 = 1 mL; 1 dm3 = 1 L
Area
square metre (m2)
10 000 cm2 = 1 m2; 10 000 m2 = 1 hectare
Mass
kilogram (kg)
1000 g = 1 kg; 1000 mg = 1 g; 1000 kg = 1 tonne
Time
second (s)
60 s = 1 min; 60 min = 1 hour
Pressure
pascal (Pa)
1000 Pa = 1 kPa
Energy
joule (J)
1000 J = 1 kJ
Careful with squares and cubes. There are 100 cm in a metre, but 10 000 cm2 in a square metre and 1 000 000 cm3 in a cubic metre. The conversion factor gets squared or cubed along with the unit.
Writing compound units properly
Any time you divide one quantity by another you make a compound unit. Rates do this constantly. The neat way to write them is with a negative index instead of a slash.
Same unit, two ways of writing it
cm3 per second = cm3/s = cm3 s−1
Oxygen produced by pondweed: cm3 s−1 or cm3 min−1.
Stomatal density: stomata mm−2.
Concentration: mol dm−3.
A rate taken from a reciprocal, where you only timed the reaction: s−1.
Take the unit straight off your working. If you divided cm3 by minutes, the unit is cm3 min−1 — you do not have to remember it, you just have to read it off the calculation you already did.
Significant figures
Significant figures are the digits in a number that are genuinely telling you something. Zeros are the awkward ones, because sometimes a zero is real information and sometimes it is just holding a space.
The rule underneath all of this: a zero counts if it is carrying real information about how precisely something was measured.
Rule
Example
All non-zero digits are significant
4.62 is 3 s.f.
Zeros between non-zero digits are significant
29.009 is 5 s.f.
Zeros before all the non-zero digits are not significant
0.00079 is 2 s.f.
Trailing zeros in a whole number with no decimal point are not significant
640 is 2 s.f.
Zeros after non-zero digits in a number with a decimal point are significant
689.0023 is 7 s.f.
🧩 Rounding to a set number of significant figures
Find the first significant figure — the first digit that is not a leading zero.
Count along from there to the number of figures you have been asked for.
Look at the next digit, the one just past where you stopped. This is your decider.
If the decider is 5 or more, round the last kept digit up. If it is 4 or less, leave it alone.
Keep any place-holding zeros so the number stays the right size.
WE 1
Rounding to significant figures
Write 0.0028461 to 3 significant figures, and 24 750 to 2 significant figures. (2 marks)
Part 1: 0.0028461
The leading zeros do not count, so the first significant figure is the 2. Counting three gives 2, 8, 4. The decider is the next digit, 6, which is 5 or more, so the 4 rounds up.
0.00285Part 2: 24 750
First two significant figures are 2 and 4. The decider is 7, so the 4 rounds up to 5. Keep the place holders.
25 000do not chop the zeros off 25 000 — without them the number would be 25, which is wrong by a factor of a thousand
Scales of magnification
Magnification questions are really unit questions in disguise. Almost every mark lost is a conversion that never happened.
Magnification
magnification = size of image ÷ actual size of object
The two sizes must be in the same unit before you divide. Magnification itself has no unit — it is just a number, written with a multiplication sign in front of it.
WE 2
Magnification with a unit conversion
A drawing of a plant cell measures 40 mm across. The real cell is 8 µm across. Calculate the magnification of the drawing. (3 marks)
Step 1: get both measurements into the same unit
The actual size is in µm, so convert the image size into µm too.
40 mm × 1000 = 40 000 µmStep 2: divide image size by actual size
40 000 ÷ 8 = 5000
×5000 (no unit)if you had divided 40 by 8 you would have written ×5 — a thousand times too small, and the examiner sees that mistake every year
WE 3
Choosing sensible units
A student writes: “The amount of oxygen collected was 0.000012 m3 in 40 seconds.” Rewrite this using sensible units and give the rate. (3 marks)
Step 1: fix the word “amount”
In science, amount means moles. This is a volume, so say volume.
Step 2: choose a unit that suits the size
1 m3 = 1 000 000 cm3, so 0.000012 m3 = 12 cm3.
Step 3: give the rate with a compound unit
12 ÷ 40 = 0.30
A volume of 12 cm3, collected at 0.30 cm3 s−112 cm3 is far easier to picture than 0.000012 m3 — good units make your answer readable
💡 Exam tips
Convert units before you start calculating, not halfway through.
Write the unit next to every number in your working, not just at the end. It stops mistakes appearing.
Use index form for compound units: cm3 s−1, mol dm−3, stomata mm−2.
Magnification is a plain number with no unit. Write it as ×5000, not 5000 µm.
Avoid “amount” unless you mean moles. Use mass, volume or concentration.
If the question asks for a set number of significant figures, do it — the last mark is often for exactly that.
⚠ Common mistakes
Muddling mm and µm. They are a factor of 1000 apart, and this single slip ruins most magnification answers.
Using 100 to convert cm2 to m2. Areas need 10 000, volumes need 1 000 000.
Writing a bare number as an answer. With no unit, it is not an answer.
Chopping the place-holding zeros off a rounded number, turning 25 000 into 25.
Rounding at every step. Errors build up. Round once, right at the end.
Saying “amount of water”. Say volume, or mass, and keep “amount” for moles.
Up next: Handling Uncertainties — why no measurement is ever exact, how to work out the uncertainty of a piece of equipment, and what error bars are really telling you.
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