Small Prefixes: Milli, Micro and Nano

Introduction

Much of chemistry happens on a scale far too small to see. Atoms and molecules are measured in nanometres; bacteria and cells in micrometres; the samples used in medical tests may be only a few microlitres. To handle these tiny quantities neatly, chemists rely on three small prefixes: milli , micro and nano . They mirror the large prefixes kilo, mega and giga, but divide by a thousand at each step instead of multiplying.

Core explanation

Milli (m) = 10⁻³ = 0.001. A millimetre is one thousandth of a metre and a milligram one thousandth of a gram. In the laboratory you meet mL (equal to cm³), mg for small masses weighed on an analytical balance, and mmol (millimoles) for small amounts of substance in titrations. A typical titration uses about 25 cm³ of a 0.1 mol dm⁻³ solution, which contains 2.5 mmol of solute.

Micro (µ) = 10⁻⁶ = 0.000 001. Micro is a thousand times smaller than milli. Its symbol is the Greek letter µ (mu). A human hair is roughly 70 µm wide, and a red blood cell is about 7 µm across. Micropipettes deliver volumes of a few µL , and trace amounts of metals in drinking water are reported in µg per litre.

Nano (n) = 10⁻⁹ = 0.000 000 001. Nano is a thousand times smaller than micro. This is the scale of molecules. A water molecule is about 0.3 nm across, and a strand of DNA is about 2 nm wide. Visible light has wavelengths from roughly 400 nm (violet) to 700 nm (red), so colours and spectra in chemistry are almost always described in nanometres. Nanotechnology is the study and use of structures between about 1 and 100 nm in size.

Each step is ÷1000.

1 m = 1000 mm = 1 000 000 µm = 1 000 000 000 nm

Going from a larger unit to a smaller one (m → mm → µm → nm) multiplies the number by 1000 at each step; going the other way divides by 1000.

Writing µ. If you cannot type µ, write "micro" in full (micrometre) rather than using a "u" or an "m", which could be misread. In handwriting, make the long tail of µ clear.

Step-by-step reasoning

To convert 0.045 mm into micrometres:

1. Note that mm → µm is one step down the ladder. 2. Moving to a smaller unit means multiplying by 1000. 3. 0.045 × 1000 = 45. 4. So 0.045 mm = 45 µm. Check: a smaller unit needs a larger number — it does.

Visual explanation

Imagine zooming in on a ruler. At normal view you see millimetre marks. Zoom a thousand times and one millimetre stretches to show a thousand micrometres, each about the width of a bacterium. Zoom another thousand times and each micrometre shows a thousand nanometres, where individual molecules become visible.

Real-world analogy

A kilometre of road, a metre stick, a millimetre on a ruler, a micrometre-thin hair and a nanometre-sized molecule are like the successive levels of a map app. Each zoom level shows detail a thousand times finer, and the prefix tells you which level you are on.

Real-world example

Blood tests often report substances in very small units. Blood glucose is measured in mmol L⁻¹, vitamin B12 in picograms per mL, and some hormones in nmol L⁻¹. A doctor reading "5.5 mmol/L" of glucose knows at once that it is a normal fasting level, because the prefix sets the scale of the number.

Why?

Why do chemists not just use the base unit with lots of decimal places? Writing 0.000 000 55 m for the wavelength of green light hides the important digits among zeros and invites copying errors. Writing 550 nm keeps the meaningful figures visible and makes comparisons between wavelengths quick and reliable.

Common misconception

"A millimole is a million moles." The prefix milli always means one thousandth, not one million: 1 mmol = 0.001 mol. It is mega (M) that means a million. Remembering that "milli" sounds like the "mille" in millimetre and that a millimetre is tiny helps avoid this slip.

Worked example

Question: A sample of a drug has a mass of 250 µg. Express this in mg and in g.

Reasoning: Going from µg to mg is one step up, so divide by 1000: 250 ÷ 1000 = 0.250 mg. Going from mg to g is another step up: 0.250 ÷ 1000 = 0.000 250 g, which is 2.50 × 10⁻⁴ g.

Answer: 0.250 mg, which is 2.50 × 10⁻⁴ g.

Quick check

1. How many nanometres are there in 1 µm? Answer: 1000 nm.

Exam focus

Titration questions often give volumes in cm³ and amounts in mmol; be ready to convert to dm³ and mol. Wavelengths of light are usually given in nm and may need converting to metres (× 10⁻⁹) before use in equations. Always check whether you are going to a larger unit (divide) or a smaller one (multiply).

Advanced insight

Below nano come pico (p, 10⁻¹²) and femto (f, 10⁻¹⁵). Bond lengths are often given in picometres: the C–H bond is about 109 pm long. An older non-SI unit, the ångström (Å, 10⁻¹⁰ m, which is 0.1 nm), is still common in crystallography because atomic spacings are conveniently a few ångströms.

Summary

Milli (m) means 10⁻³, micro (µ) 10⁻⁶ and nano (n) 10⁻⁹, each a thousand times smaller than the previous one. Chemists use mL, mg and mmol for laboratory samples, µm and µL for cells and micro-samples, and nm for molecules and light wavelengths. Moving to a smaller unit multiplies the number by 1000 per step.

Practice questions

1. Write 0.005 g in mg and in µg. Answer: 0.005 × 1000 = 5 mg; 5 × 1000 = 5000 µg. 2. Red light has a wavelength of about 700 nm. Express this in metres using scientific notation. Answer: 700 × 10⁻⁹ m = 7.00 × 10⁻⁷ m. 3. A titration uses 3.2 mmol of acid. How many moles is this? Answer: 3.2 ÷ 1000 = 0.0032 mol. 4. Why should you avoid writing "um" for micrometre? Answer: It could be misread as another unit or a typing error; the correct symbol is µm, or the full word "micrometre" if µ is unavailable.