IB Biology SLSkill Set 3 — Maths for BiologyPaper 1 & 2Core skill~9 min read
Units, Symbols & Values
Biology runs from molecules a few nanometres across to ecosystems measured in kilometres, so you spend a lot of time sliding numbers up and down by factors of a thousand. Get the prefix wrong and a perfectly good calculation becomes a cell the size of a football. This page is about writing numbers so they mean exactly what you intend.
📘 What you need to know
The SI system is the international standard, built on a small set of base units.
Prefixes stand for powers of ten: kilo, centi, milli, micro, nano.
Standard form is written as a × 10n, where a is at least 1 and below 10.
Significant figures are the digits that actually carry information; there are firm rules for which zeros count.
Approximation means settling for a close-enough value; estimation means making a reasoned judgement when you cannot measure at all.
1 cm3 = 1 ml and 1 dm3 = 1 litre. These two show up constantly.
“Amount” has a specific meaning in science — it means moles. Say mass, volume or concentration if that is what you mean.
SI base units
Every other unit in science is built from these. You do not need to recite the list, but you should recognise each one and its symbol.
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
Everyday biology mostly uses units derived from these: grams for mass, degrees Celsius for temperature, cm3 for volume, and combinations such as mol dm−3 for concentration.
Notice that the base unit of mass is the kilogram, not the gram — the only base unit that already has a prefix built into it. Do not let that trip you up in a conversion.
Prefixes and converting between them
Prefix
Symbol
Power of ten
Means
kilo-
k
103
a thousand times bigger
centi-
c
10−2
a hundredth
milli-
m
10−3
a thousandth
micro-
µ
10−6
a millionth
nano-
n
10−9
a thousand millionth
That last line is the quickest self-check there is. Smaller unit, bigger number — if you have both getting smaller, you have divided when you should have multiplied.
WORKED EXAMPLE
A student measures a plant cell as 0.045 mm long. Convert this to micrometres, then to metres in standard form.
Step 1: millimetres to micrometres — a smaller unit, so multiply0.045 × 1000 = 45 µmStep 2: millimetres to metres — a bigger unit, so divide0.045 ÷ 1000 = 0.000045 mStep 3: write it in standard form0.000045 = 4.5 × 10−5 m45 µm, or 4.5 × 10−5 m45 µm is a believable plant cell. If you had got 45 000 µm, that is 4.5 cm — a cell you could see across the room.
Standard form
Also called scientific notation. It is how you write numbers that are far too big or far too small to sit comfortably on a page.
The sign of the power is the whole message: positive for numbers bigger than ten, negative for numbers smaller than one.
a must be at least 1 and less than 10. So 4.5 × 10−5, never 45 × 10−6.
A positive n tells you how many times a is multiplied by 10.
A negative n tells you how many times a is divided by 10.
Standard form also makes significant figures obvious, which is why it is worth using in answers.
Significant figures
Significant figures are the digits that carry real information about the size of a number. The rules all come down to which zeros are doing a job and which are just holding a place.
🧩 The rules, in order
Every non-zero digit counts. Always.
Zeros between non-zero digits count. 4107 has 4 s.f.
Leading zeros never count. They only position the decimal point, so 0.00420 has 3 s.f.
Trailing zeros in a whole number with no decimal point do not count. 57 000 has 2 s.f.
Trailing zeros after a decimal point do count. 689.0023 has 7 s.f.
Rewrite 57 000 as 5.7 × 104 and the two significant figures are impossible to miscount.
Rounding to a number of significant figures
Find the first significant figure and count along to the one you need.
Look at the next digit — the decider.
If the decider is 5 or more, round the last kept digit up. Otherwise leave it.
WORKED EXAMPLE
Write 0.024561 to 3 significant figures.
Step 1: find the first significant figure
The leading zeros do not count, so counting starts at the 2.
Step 2: count three significant figures2, 4, 5 — so we keep 0.0245Step 3: check the decider
The next digit is 6, which is 5 or more, so round the 5 up.
0.0246Keep the leading zeros in your written answer. They are not significant figures, but they are still holding the decimal point in place.
Writing units properly
Leave a space between the number and the unit: 25 g, not 25g.
“Per” becomes a negative power. Bubbles per minute is written as bubbles min−1, moles per cubic decimetre as mol dm−3.
Area: 10 000 m2 = 1 hectare, which is the usual unit for a field site.
Time: 60 s in a minute, 60 min in an hour. Convert before you calculate a rate, not after.
Units go in the column heading of a table, not next to every number.
Watch the word “amount”. In science, amount means a number of moles. If you mean how heavy, say mass; how much liquid, say volume; how strong, say concentration. Examiners notice.
WORKED EXAMPLE
How many moles of glucose are there in 20 cm3 of a 0.25 mol dm−3 solution?
Step 1: the concentration is per dm3, so convert the volume first20 ÷ 1000 = 0.020 dm3Step 2: multiply concentration by volume0.25 × 0.020 = 0.0050.005 mol, or 5 × 10−3 molThe units in the concentration tell you which volume unit to use. Miss that step and your answer is out by a factor of 1000.
Approximation and estimation
These two words get used interchangeably in everyday speech, but they describe different situations.
Approximation means accepting a value close to the true one because working it out exactly would be slow and would not change the conclusion. Rounding a magnification to “about ×400” is an approximation.
Estimation means making a reasoned judgement when the true value cannot be measured directly. Biologists estimate when the first living cells appeared, or how long ago two species diverged, using evidence such as the molecular clock.
Both are respectable science, as long as you say which you have done and why. An estimate with a stated basis is far stronger than a precise-looking number with no justification behind it.
💡 Exam tip
Convert units before you calculate, and write the unit at every step so you can see where it went wrong.
Check the direction: smaller unit means a bigger number.
Give answers to the number of significant figures the question asks for — and if it does not say, match the raw data.
Use standard form for anything below 0.001 or above 10 000; it is clearer and it shows your significant figures.
Write rates with negative powers: cm3 s−1, not “cm3 per s”.
Sanity-check the answer against biology. A cell is micrometres, an organelle is nanometres.
⚠ Common mix-up
Multiplying instead of dividing when moving up to a larger unit.
Treating cm3 and dm3 as a factor of 10 apart. They are 1000 apart, because the unit is cubed.
Writing 45 × 10−6 and calling it standard form. The first part must be below 10.
Counting leading zeros as significant. 0.00420 has three, not six.
Rounding partway through a calculation, then rounding again at the end — the error builds up.
Giving more significant figures than your instrument justifies. A ruler reading to the nearest mm does not support four decimal places.
Using “amount” loosely when you mean mass, volume or concentration.
Up next: Handling Uncertainties — what ± really means, how to combine uncertainties, and how to read error bars and correlations honestly.
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