Millimetres, micrometres, nanometres

Ordinary rulers stop at the millimetre. To measure germs we need smaller units. Each one is 1,000 times smaller than the one before:

• 1 millimetre (mm) = 10⁻³ m, one thousandth of a metre
• 1 micrometre (µm) = 10⁻⁶ m = 0.001 mm, one millionth of a metre
• 1 nanometre (nm) = 10⁻⁹ m = 0.001 µm, one billionth of a metre

The Greek letter µ (say "mu") stands for "one millionth". Take care: µm is not mm. A bacterium that is 2 µm long is 0.002 mm long. Mixing these up makes an answer 1,000 times too big or too small, one of the most common mistakes on exams.

To change units, move the decimal place by three:

• 3 µm = 3 × 1,000 = 3,000 nm
• 70 µm = 70 ÷ 1,000 = 0.07 mm
• 100 nm = 0.1 µm

How many fit inside? Divide the big size by the small size, using the same unit. A bacterium that is 2 µm long is 2,000 nm. A virus particle that is 100 nm across fits into that length 2,000 ÷ 100 = 20 times if you line them up end to end. Along 1 mm (1,000 µm) you could line up 1,000 ÷ 2 = 500 E. coli bacteria, end to end.