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How do you dilute a sample millions of times in steps, and use the dilution to count the cells in the original?

Describe serial dilution and use the dilution factor to calculate concentrations and cell numbers

A focused answer to the O-Level outcome on serial dilution. How a step-by-step dilution series works, dilution factors, and how to calculate the cell number in the original sample.

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
Try this

What this dot point is asking

This outcome asks you to describe serial dilution and to use the dilution factor to work out concentrations and cell numbers. It is a core quantitative skill: cultures contain far too many cells to count directly, so you dilute in steps until they are countable, then scale back up. Examiners reward clear, laid-out working.

The answer

What a serial dilution is

A serial dilution is a stepwise dilution in which a sample is diluted by the same factor repeatedly. A common scheme is a tenfold dilution at each step:

Transfer $1\ \text{mL}$ of the sample into $9\ \text{mL}$ of liquid, giving a total of $10\ \text{mL}$ .
This is a tenfold ( $\times\frac{1}{10}$ ) dilution: the concentration falls by a factor of $10$ .
Repeat using $1\ \text{mL}$ of that tube into the next $9\ \text{mL}$ , and so on.

Dilution factor

The dilution factor tells you how many times more dilute the sample is than the original.

One tenfold step has a dilution factor of $10$ .
The total dilution factor is the product of all the steps. Two tenfold steps give $10\times10 = 100$ ; three give $1000$ , and so on.

Why it is used for counting

A culture may contain millions of cells per millilitre, far too many to count, the colonies would merge on a plate. Diluting in steps reduces the number until a sample gives a countable number of separate colonies. Each colony is assumed to have grown from one cell.

Calculating the original number

To find the number of cells per millilitre in the original culture:

Count the colonies on the plate (each is one cell from the diluted sample).
Divide by the volume plated to get cells per millilitre of the diluted culture.
Multiply by the total dilution factor to scale back to the original.

Counting bacteria from a diluted plate

A culture is diluted in three tenfold steps. A $0.1\ \text{mL}$ sample of the final dilution is spread on a plate and grows $45$ colonies. Find the number of bacteria per millilitre in the original culture.

Step 1: Find the total dilution factor

Three tenfold steps give a total dilution factor of $10\times10\times10 = 1000$ .

Step 2: Use the colony count

Each colony grew from one bacterium, so the $0.1\ \text{mL}$ sample contained $45$ bacteria.

Step 3: Convert to per millilitre of the dilution

\frac{45}{0.1} = 450\ \text{bacteria per mL of the diluted culture}

Step 4: Scale back to the original

Multiply by the total dilution factor:

450 \times 1000 = 450\,000 = 4.5\times10^{5}\ \text{bacteria per mL}

So the original culture had about $4.5\times10^{5}$ bacteria per millilitre. Finding the dilution factor, dividing by the plated volume, and multiplying back up is exactly what the question rewards.

Examples in context

Example 1. Quality control of a culture. In a factory, the number of cells in a fermenter is checked by serial dilution and plating, so the process can be kept at the right cell density. The dilution-factor calculation turns a handful of colonies into an accurate count of billions.

Example 2. Testing water safety. Water can be tested for bacteria by diluting and plating, then counting colonies and scaling up. A count above a safe limit signals contamination, showing the same technique used to protect public health.

Try this

Q1. State the total dilution factor of four tenfold dilution steps. [1 mark]

Cue. $10\times10\times10\times10 = 10\,000$ .

Q2. A $0.1\ \text{mL}$ sample of a culture diluted $100$ times grows $30$ colonies. Find the number of bacteria per millilitre in the original. [3 marks]

Cue. $30 \div 0.1 = 300$ per mL of the dilution; $300 \times 100 = 30\,000 = 3\times10^{4}$ bacteria per mL.

Q3. Explain why a culture is diluted before the bacteria are counted on a plate. [2 marks]

Cue. The original has too many cells to count, so the colonies would merge; diluting reduces the number to a countable set of separate colonies.

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.

Original5 marksExplain what a serial dilution is and why it is used when counting bacteria in a culture.

Show worked answer →

Examiners want the meaning of a serial dilution and the reason for using one.

A serial dilution is a stepwise dilution, where a sample is diluted by the same factor repeatedly. For example, each step might transfer $1\ \text{mL}$ of the previous tube into $9\ \text{mL}$ of liquid, giving a tenfold dilution each time, so the concentration falls by $10$ at every step.

It is used when counting bacteria because the original culture has far too many cells to count, the colonies would merge on a plate. By diluting in steps, the number of cells is reduced until a sample gives a countable number of separate colonies. Counting those, and multiplying back by the total dilution factor, gives the number in the original.

What markers reward: a serial dilution as repeated dilution by the same factor (for example tenfold each step), the reason that the original has too many cells to count directly, and the idea that diluting gives a countable number that is scaled back up using the dilution factor.

Original5 marksA bacterial culture is diluted by a total factor of

10\,000

. A

0.1\ \text{mL}

sample of the diluted culture is spread on a plate and grows

60

colonies. Calculate the number of bacteria per millilitre in the original culture, showing your working.

Show worked answer →

The answer should scale up by both the dilution factor and the sample volume.

Each colony grew from one bacterium, so the $0.1\ \text{mL}$ diluted sample contained $60$ bacteria.

First, find the number per millilitre of the diluted culture: $60 \div 0.1 = 600$ bacteria per mL.

Then multiply by the total dilution factor to get back to the original: $600 \times 10\,000 = 6\,000\,000 = 6\times10^{6}$ bacteria per mL.

What markers reward: treating each colony as one bacterium, dividing by the sample volume to get per millilitre ( $600$ ), multiplying by the dilution factor ( $\times10\,000$ ) to give $6\times10^{6}$ bacteria per mL, with correct working and units.