GCSE · Biology · Edexcel · Spec 1BI0

Number, size and scale in biology

Which is longer: 9 mm or 90 µm? If your gut said 90, you've met the trap this lesson fixes. In biology, numbers only make sense with their units.

From virus to frog egg

Tap each one to see how big it really is. Every tick is ten times the one before. Anything smaller than about 100 µm needs a microscope; the frog egg, at about 1 mm, you can see with your own eyes.

Virus

about 10–100 nm

Viruses are tiny, even next to bacteria, so we measure them in nanometres. They aren't considered living. Ribosomes inside cells (about 20–30 nm) live down here too.

Climb the unit ladder

One palisade cell, four ways to write it

A palisade cell is about 70 µm long. Write its length in nanometres, in millimetres, and in metres using standard form. The ladder runs m → mm → µm → nm, with a factor of 1000 between neighbouring rungs.

Start where we are: 70 µm. Nanometres are one rung below micrometres; millimetres and metres are above.1 mm = 1000 µm and 1 µm = 1000 nm.
missing step

Which line is step 2?

µm → nm is one rung down, so multiply by 1000: 70 × 1000 = 70 000 nmµm → nm is one rung down, so multiply by 100: 70 × 100 = 7000 nmµm → nm is two rungs down, so multiply by 1 000 000: 70 000 000 nm

What do you really think?

Reading 2.6 × 10⁻³ mm

A cell is 2.6 × 10⁻³ mm long.

Which of these is closest to what you think right now?

The −3 means it's a negative length, less than zero.To write it in µm, I divide by 1000, because µm is the smaller unit.It's a tiny positive length: 0.0026 mm, which is 2.6 µm or 2600 nm.10⁻³ means move the decimal point 3 places to the right, so it's 2600 mm.

How sure are you?

I'm sureI think soI'm guessing

The −3 means it's a negative length, less than zero.

This is a common misconception

The minus sign isn't about the length at all. A negative power means 'divide by 10 that many times': 2.6 ÷ 10 ÷ 10 ÷ 10 = 0.0026. So a negative power gives a small number, never a negative one.

To write it in µm, I divide by 1000, because µm is the smaller unit.

This is a common misconception

Flip it round: a smaller unit means you need MORE of them to cover the same length. 1 mm holds 1000 µm, so going to the smaller unit multiplies by 1000: 0.0026 × 1000 = 2.6 µm. If your number shrank when the unit shrank, go back.

It's a tiny positive length: 0.0026 mm, which is 2.6 µm or 2600 nm.

This matches the evidence

Exactly. Same cell, written three ways: 2.6 × 10⁻³ mm = 2.6 µm = 2.6 × 10³ nm. The power went from −3 to +3 only because the unit got smaller. The cell didn't change.

10⁻³ means move the decimal point 3 places to the right, so it's 2600 mm.

This is a common misconception

That's what 10³ does. The minus sign flips it: 10⁻³ moves the point 3 places LEFT, so it's 0.0026 mm. You'll see 2600 in the right answer, but only in nanometres: 2600 nm = 2.6 × 10³ nm.

Negative power → small number. Smaller unit → bigger number. If an answer breaks either rule, check which way you went.

Gut feeling vs the numbers

How many times longer?

An ant is about 9 mm long. An amoeba, a single-celled organism, is about 90 µm long. How many times longer is the ant than the amoeba?

Your estimate

500 times

An ant is about 9 mm long. An amoeba, a single-celled organism, is about 90 µm long. How many times longer is the ant than the amoeba? Estimate between 0 times and 1000 times.

0 times1000 times

Spot the slip

Where does this magnification go wrong?

A cell is 90 µm long. In a drawing, the same cell is 18 mm long. Calculate the magnification of the drawing.

A student's answer — which line goes wrong?

magnification = size of image ÷ size of real object
size of image = 18 mm; size of real object = 90 µm
magnification = 18 ÷ 90
= 0.2
magnification = ×0.2

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

From a virus to a frog egg: one scale, four units, and the rule that makes every comparison work. Same unit first.

What you need to know

Most animals and plants are multicellular (millions, 10⁶, or billions, 10⁹, of cells); unicellular organisms are a single cell and are microscopic.
Objects from about 1 nm to about 100 µm are microscopic; bigger things, like a frog egg (about 1 mm), can be seen with the unaided eye.
1 m = 1000 mm, 1 mm = 1000 µm and 1 µm = 1000 nm. In standard form: 1 mm = 1 × 10⁻³ m, 1 µm = 1 × 10⁻⁶ m, 1 nm = 1 × 10⁻⁹ m.
To go to a smaller unit, multiply by 1000 per step; to go to a larger unit, divide by 1000 per step.
Magnification = size of image ÷ size of real object, with both sizes in the same unit.

The big picture

Living things and their parts span a huge range of sizes. Most cells are microscopic, so biologists use millimetres, micrometres and nanometres (each a thousand times smaller than the one before) and standard form to keep numbers manageable. To compare two sizes or calculate magnification, put both into the same unit first, then divide.

Key points

1Viruses (about 10–100 nm) are much smaller than bacteria (about 1–10 µm), and eukaryotic cells such as red blood cells (7–9 µm), palisade cells (about 70 µm) and human egg cells (about 118–120 µm) are larger again.

2Pick the unit that keeps the number manageable: micrometres for bacteria, nanometres for ribosomes (about 20–30 nm).

3Standard form is A × 10ⁿ with A at least 1 and less than 10. A negative power means a small number, not a negative one.

4How many times bigger? Convert to the same unit, then divide the larger size by the smaller.

5Rearranged: size of image = magnification × size of real object; size of real object = size of image ÷ magnification. Answers may need to be given in standard form.

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Worked example

Problem

A drawing of a cell is 24 mm long. The drawing has a magnification of ×400. What is the real length of the cell in µm?

⚠ Watch out

Comparing or dividing two sizes while they are still in different units. 6 mm and 30 µm are not '6 and 30': convert one so both share a unit, then divide.

🧠

Memory hook

Smaller unit, bigger number. It's like paying in pennies instead of pounds: the amount stays the same, but the number you write goes up.

✓

Check yourself

A bacterium is 3 µm long. Write its length in nanometres, in millimetres, and in metres using standard form. Then work out how many times longer a 0.3 mm cell is.

Flashcards

(13)

Multicellular vs unicellular?

Multicellular organisms (most animals and plants) are made of millions (10⁶) or billions (10⁹) of cells. Unicellular organisms are one cell and are microscopic.

Roughly where does 'microscopic' end?

About 100 µm. Things from about 1 nm to about 100 µm need a microscope; a frog egg (about 1 mm) can be seen with the unaided eye.

The unit ladder, largest to smallest

m → mm → µm → nm, with a factor of 1000 between neighbouring units (1 m = 1 000 000 µm = 1 000 000 000 nm).

mm, µm and nm as fractions of a metre, in standard form

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

Converting to a smaller unit: multiply or divide?

Multiply by 1000 for each step down (smaller unit, bigger number). Going to a larger unit, divide by 1000 per step.

What is standard form?

A × 10ⁿ, where A is at least 1 and less than 10 and n is the power of 10.

What does a negative power of ten tell you?

The number is small (less than 1), not negative. 2.6 × 10⁻³ = 0.0026.

Which unit suits a bacterium, and which a ribosome?

Micrometres for bacteria (E. coli about 1–2 µm); nanometres for ribosomes (about 20–30 nm).

How big are viruses, and are they living?

About 10–100 nm, smaller than bacteria. Viruses are not considered living.

Prokaryotic vs eukaryotic cell size

Bacteria (prokaryotes) are about 1–10 µm; eukaryotic cells are larger, e.g. red blood cell 7–9 µm, palisade cell about 70 µm.

How do you find how many times bigger one thing is than another?

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

Magnification: meaning and formula

How many times an object has been enlarged. Magnification = size of image ÷ size of real object, both in the same unit.

Rearranging the magnification formula

Size of image = magnification × size of real object. Size of real object = size of image ÷ magnification.

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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One palisade cell, four ways to write it

Reading 2.6 × 10⁻³ mm

How many times longer?

Where does this magnification go wrong?

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