GCSE · Biology · Edexcel · Spec 1BI0

Quantitative units in cell biology

A bacterium can be just 1 micrometre long. Line up a thousand of them end to end, and the whole queue is only one millimetre long.

The map of tiny sizes

Where does each unit live?

This line is a map of sizes. Each number is a power of ten of a metre: the mark at −3 means 10⁻³ m, which is a thousandth of a metre. Slide each unit to where you think it lives, then place the virus and the bacterium. (Tip: ten of something is one place to the right of it.) Then check.

m — 1 metremm — 1 millimetreµm — 1 micrometrenm — 1 nanometrevirus — A virus 10 nm acrossbact — A bacterium 10 µm long

Choosing a unit

Which unit fits?

Pick a structure, then choose the unit that keeps its size a sensible number. Or decide it's big enough to see without a microscope.

Still to sort

Measure in nanometres (nm) (0)

Tiny structures, tens of nanometres across

Where the line is: 1,000 nm make 1 µm. Anything well under a micrometre turns into an awkward decimal in µm, so switch to nm.

Measure in micrometres (µm) (0)

Whole cells that still need a microscope

Where the line is: Structures up towards 100 µm are still microscopic, too small to see with the unaided eye.

Visible to the unaided eye (0)

Big enough to see without a microscope

Where the line is: A frog egg, and anything larger, can be seen with the human eye.

6 of 6 still to sort.

Most cells are too small to see with the unaided eye, so they need a microscope. But which ruler do you measure them with?

Watch out: A sensible unit is one that avoids fiddly decimals and long strings of zeros. The size itself doesn't change. Only the way you write it changes.

Standard form

What does the power really mean?

Standard form writes any number as A × 10ⁿ. A is a number from 1 up to, but not including, 10. The power, n, counts how many times the number has been multiplied or divided by 10. So 1,000 is 1 × 10³ and a micrometre is 1 × 10⁻⁶ m. Most animals and plants are made of millions or billions of cells. A million is 10⁶, and a billion is 10⁹: a 1 followed by nine zeros, or 1,000 million.

Which idea about the powers in standard form is closest to what you think right now?

10⁻⁶ is a negative number. The minus sign means it's less than zero.0.0026 should be 2.6 × 10³, because the decimal point moved three places.1 × 10³ isn't proper standard form, because A has to be bigger than 1.A negative power means a small number (divided by 10). A positive power means a large number (multiplied by 10).

How sure are you?

I'm sureI think soI'm guessing

10⁻⁶ is a negative number. The minus sign means it's less than zero.

This is a common misconception

Easy trap! The minus sign belongs to the power, not to the number. 10⁻⁶ means 1 divided by 10 six times, which is 0.000001. That's tiny, but it's still more than zero. A micrometre is just a very small length, not a negative one.

0.0026 should be 2.6 × 10³, because the decimal point moved three places.

This is a common misconception

You've counted the places perfectly. It's the direction that's flipped. 2.6 × 10³ is 2,600, a large number. 0.0026 is small: it's 2.6 divided by 10 three times, so it's 2.6 × 10⁻³. Quick check: small number → negative power, large number → positive power.

1 × 10³ isn't proper standard form, because A has to be bigger than 1.

This is a common misconception

Nearly, but A is allowed to be exactly 1. The rule is 1 ≤ A < 10, so from 1 up to, but not including, 10. That makes 1 × 10³ perfectly good standard form for 1,000. What A can't be is 10 or more: 10 × 10² is not standard form.

A negative power means a small number (divided by 10). A positive power means a large number (multiplied by 10).

This matches the evidence

Spot on. 1 × 10⁻⁶ m is a millionth of a metre, because 1 has been divided by 10 six times. 10⁹ cells is a billion, because 1 has been multiplied by 10 nine times: 1,000,000,000, or 1,000 million. The sign on the power just tells you which way you went.

Minus power: divided by 10 that many times, so a small number. Plus power: multiplied by 10 that many times, so a large number. And A always runs from 1 up to, but not including, 10.

Converting units

Your turn to fill the gaps

An amoeba is 90 µm across. Write its size in nanometres, then in millimetres. Give each answer in standard form.

Nanometres first. A nanometre is smaller than a micrometre, so it takes more of them to span the amoeba. The number must get bigger.Always decide the direction before you calculate.
missing step

Which line is step 2?

µm → nm is one step to a smaller unit, so multiply by 1,000: 90 × 1,000 = 90,000 nm.µm → nm is one step to a smaller unit, so divide by 1,000: 90 ÷ 1,000 = 0.09 nm.µm → nm is two steps down, so multiply by 1,000,000: 90 × 1,000,000 = 90,000,000 nm.

Comparing sizes

Bacterium versus virus

A bacterium is 1 µm long. A virus is 100 nm across. How many times longer is the bacterium than the virus? Commit to a number before you convert anything.

Your estimate

60 times

A bacterium is 1 µm long. A virus is 100 nm across. How many times longer is the bacterium than the virus? Commit to a number before you convert anything. Estimate between 0 times and 120 times.

0 times120 times

Watch out: Never divide two sizes that are written in different units. Convert first, then divide.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

The four units in order (metre, millimetre, micrometre, nanometre), and that each one is one thousandth of the one before.
Each unit's size in metres in standard form: 1 mm = 1 × 10⁻³ m, 1 µm = 1 × 10⁻⁶ m, 1 nm = 1 × 10⁻⁹ m.
How to convert between units by multiplying or dividing by 1,000 for each step.
How to write very large and very small numbers in standard form, and what a negative or positive power means.
How to choose a sensible unit for a structure, and how to compare two sizes by converting to the same unit and dividing.

The big picture

Most cells are too small to see unaided, so we measure them in micrometres (µm) and nanometres (nm). The units m, mm, µm and nm fall in equal steps: each is one thousandth of the one before, so 1 mm = 1 × 10⁻³ m, 1 µm = 1 × 10⁻⁶ m and 1 nm = 1 × 10⁻⁹ m. Converting means × 1,000 for each step to a smaller unit and ÷ 1,000 for each step to a larger one. Standard form (A × 10ⁿ, with 1 ≤ A < 10) keeps huge and tiny numbers readable. To compare two sizes, use one unit, then divide.

Key points

1Most cells are too small to see with the unaided eye, so we need a microscope to observe them. Cells and subcellular structures are measured in micrometres (µm) and nanometres (nm).

2m → mm → µm → nm: each unit is one thousandth of the next larger one. A metre holds 1,000 mm, a million µm and a billion nm.

3Going to a smaller unit: × 1,000 per step, so the number gets bigger. Going to a larger unit: ÷ 1,000 per step, so the number gets smaller.

4Standard form is A × 10ⁿ with 1 ≤ A < 10. A negative power shows a small number and a positive power shows a large number. A million is 10⁶ and a billion is 10⁹.

5Viruses are 10–100 nm across and aren't considered living things. Bacteria (unicellular prokaryotes) are 1–10 µm. Eukaryotic cells are larger. Structures up towards 100 µm are microscopic, and a frog egg and anything larger can be seen with the eye.

6To compare two sizes, convert both to the same unit, then divide the larger by the smaller.

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Worked example

Problem

A ribosome is roughly 20–30 nm across. Take one that is 25 nm across. Write its size in metres, in standard form.

⚠ Watch out

Multiplying when you should divide (or the other way round). Going to a smaller unit makes the number bigger (× 1,000 per step); going to a larger unit makes it smaller (÷ 1,000 per step). Before you calculate, ask: should my answer be a bigger or a smaller number?

🧠

Memory hook

Milli, micro, nano: minus three, minus six, minus nine. Every step down the ladder is three more places, a thousand times smaller. Smaller unit, bigger number.

✓

Check yourself

Cover the page. Put m, mm, µm and nm in order and give each one's power of ten in metres. Then convert 4 µm into nanometres and into millimetres, writing both answers in standard form.

Flashcards

(12)

Put these units in order from largest to smallest: nm, m, µm, mm.

m, mm, µm, nm. Each unit is one thousandth of the one before it.

What are 1 mm, 1 µm and 1 nm in metres, in standard form?

1 mm = 1 × 10⁻³ m, 1 µm = 1 × 10⁻⁶ m, 1 nm = 1 × 10⁻⁹ m.

How many mm, µm and nm are there in one metre?

1,000 millimetres, a million micrometres and a billion nanometres.

How do you convert between neighbouring units, such as µm to nm, or µm to mm?

To the next smaller unit, multiply by 1,000 (the number gets bigger). To the next larger unit, divide by 1,000 (the number gets smaller).

What is standard form?

A way of writing very large or very small numbers as A × 10ⁿ, where A is from 1 up to, but not including, 10 (1 ≤ A < 10).

What does a negative power of ten tell you in standard form?

The number is small: it has been divided by 10 that many times. A negative power does not make the number negative.

What are a million and a billion as powers of ten?

A million is 10⁶ (1 followed by six zeros). A billion is 10⁹ (1 followed by nine zeros, or 1,000 million).

How do you work out how many times larger one structure is than another?

Convert both sizes to the same unit, then divide the larger size by the smaller.

How big are viruses, and are they living things?

Between 10 and 100 nanometres. Viruses are not considered to be living things.

How big are bacteria, and what kind of cell are they?

Between 1 and 10 micrometres. Bacteria are prokaryotes, and each one is a single cell (unicellular).

Why are nanometres the better unit for a ribosome?

A ribosome is only about 20–30 nm across, much smaller than a bacterium. In micrometres it would be an awkward decimal (0.02–0.03 µm).

What is a unicellular organism, and can you see one without a microscope?

An organism made of only one cell. Unicellular organisms are microscopic, so you need a microscope.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Where does each unit live?

Which unit fits?

What does the power really mean?

Your turn to fill the gaps

Bacterium versus virus

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