Convert 0.03\ mm to micrometres. [1 mark]

A culture contains 510^6 cells per millilitre. How many cells are in 200\ mL? [2 marks]

SEAB Original-style practice: A bacterial cell is 2\ μm long and a typical animal cell is 20\ μm across. (a) Convert each length to millimetres. (b) State how many times longer the animal cell is than the bacterial cell.

Examiners want correct conversions and a sensible ratio. (a) There are 1000\ μm in a millimetre. The bacterial cell is 2 1000 = 0.002\ mm. The animal cell is 20 1000 = 0.02\ mm. (b) The animal cell is 20 2 = 10 times longer than the bacterial cell. What markers reward: dividing micrometres by 1000 to get millimetres, both conversions correct with units, and the ratio worked out as a simple number with no unit.

SingaporeBiotechnologySyllabus dot point

Cells and molecules are far too small to see, so how do we measure and talk about their size in a laboratory?

Use appropriate units to describe the size of cells, molecules and laboratory volumes, and convert between them

A focused answer to the O-Level outcome on scale and units. The units used for cells, molecules and volumes, how to convert between them, and how to estimate the number of cells in a culture.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
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What this dot point is asking

This outcome asks you to use the right units to describe very small things, from molecules and cells to the tiny volumes handled in molecular biology, and to convert between those units. Biotechnology works at scales far below what the eye can see, so being fluent with these units, and their conversions, is a basic survival skill in the laboratory.

The answer

Units of length

Because cells and molecules are tiny, we use submultiples of the metre:

Millimetre (mm) is one thousandth of a metre, written $10^{-3}\ \text{m}$ .
Micrometre (um, written $\mu\text{m}$ ) is one millionth of a metre, $10^{-6}\ \text{m}$ . Cells are typically a few to a few tens of micrometres.
Nanometre (nm) is one billionth of a metre, $10^{-9}\ \text{m}$ . Molecules and viruses are measured in nanometres.

Each step down is a factor of $1000$ : $1\ \text{mm} = 1000\ \mu\text{m}$ and $1\ \mu\text{m} = 1000\ \text{nm}$ .

Units of volume

In molecular biology the volumes are tiny, so we work below the litre:

Millilitre (mL) is one thousandth of a litre.
Microlitre (uL, written $\mu\text{L}$ ) is one millionth of a litre. Reagents are measured in microlitres with a micropipette.

Again each step is a factor of $1000$ : $1\ \text{L} = 1000\ \text{mL}$ and $1\ \text{mL} = 1000\ \mu\text{L}$ .

A sense of scale

Holding the scale in mind helps you check that an answer is sensible:

A bacterial cell is about $1$ to $5\ \mu\text{m}$ .
An animal or plant cell is about $10$ to $100\ \mu\text{m}$ .
A virus is about $20$ to $300\ \text{nm}$ .
A DNA molecule is about $2\ \text{nm}$ wide.

Converting between units

To go from a larger unit to a smaller one, multiply. To go from a smaller unit to a larger one, divide. Because each step is a factor of $1000$ , conversions are quick once you know which way to move.

Estimating the number of cells in a culture

A flask holds $500\ \text{mL}$ of bacterial culture. A sample is counted and found to contain $8\times10^{6}$ cells per millilitre. Work out the total number of cells in the flask, and express it in standard form.

Step 1: Identify what is known

The concentration is $8\times10^{6}$ cells per millilitre, and the volume is $500\ \text{mL}$ .

Step 2: Choose the operation

Total number equals concentration multiplied by volume, because each millilitre contributes the same number of cells.

Step 3: Multiply

N = 8\times10^{6}\ \text{cells mL}^{-1} \times 500\ \text{mL} = 4000\times10^{6}\ \text{cells}

Step 4: Write in standard form

$4000\times10^{6}$ is $4\times10^{9}$ . So the flask holds about $4\times10^{9}$ cells, that is four billion cells.

This shows why standard form is essential in biotechnology: the numbers are far too large or small to write out comfortably in full.

Examples in context

Example 1. Reading a microscope scale. A student measures a cell as $0.05\ \text{mm}$ across. Converting to micrometres by multiplying by $1000$ gives $50\ \mu\text{m}$ , a sensible size for a plant cell. The conversion turns an awkward decimal into a familiar value.

Example 2. Setting up a PCR. A polymerase chain reaction is mixed in a $25\ \mu\text{L}$ tube, with each ingredient added in microlitre amounts. Working in microlitres rather than millilitres keeps the numbers as easy whole values and matches what a micropipette can deliver.

Try this

Q1. Convert $0.03\ \text{mm}$ to micrometres. [1 mark]

Cue. Multiply by $1000$ : $0.03\times1000 = 30\ \mu\text{m}$ .

Q2. A culture contains $5\times10^{6}$ cells per millilitre. How many cells are in $200\ \text{mL}$ ? [2 marks]

Cue. $5\times10^{6}\times200 = 1000\times10^{6} = 1\times10^{9}$ cells.

Q3. State the most suitable unit for measuring (a) the width of a DNA molecule and (b) the volume of a reagent in a PCR. [2 marks]

Cue. (a) Nanometres, because DNA is about $2\ \text{nm}$ wide. (b) Microlitres, because PCR reagents are tiny volumes added with a micropipette.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marksA bacterial cell is

2\ \mu\text{m}

long and a typical animal cell is

20\ \mu\text{m}

across. (a) Convert each length to millimetres. (b) State how many times longer the animal cell is than the bacterial cell.

Show worked answer →

Examiners want correct conversions and a sensible ratio.

(a) There are $1000\ \mu\text{m}$ in a millimetre. The bacterial cell is $2 \div 1000 = 0.002\ \text{mm}$ . The animal cell is $20 \div 1000 = 0.02\ \text{mm}$ .

(b) The animal cell is $20 \div 2 = 10$ times longer than the bacterial cell.

What markers reward: dividing micrometres by 1000 to get millimetres, both conversions correct with units, and the ratio worked out as a simple number with no unit.

Original4 marksExplain why the micrometre and the microlitre are convenient units in a biotechnology laboratory, giving one thing each is used to measure.

Show worked answer →

The answer should link each unit to the scale of the thing it measures.

The micrometre, one millionth of a metre, is convenient because cells are about this size, so cell measurements come out as small whole numbers rather than tiny fractions of a metre. For example, a bacterial cell is a few micrometres long.

The microlitre, one millionth of a litre, is convenient because the volumes handled in molecular biology are tiny, so reagents and samples are measured in microlitres with a micropipette. For example, a polymerase chain reaction may use a $25\ \mu\text{L}$ reaction volume.

What markers reward: the idea that each unit matches the scale of what it measures so values are easy to handle, with a correct example of something measured in micrometres (a cell) and in microlitres (a small reaction or sample volume).