Scientists around the world use one system of units, the SI (from the French Système International). Its base units include the meter (m), kilogram (kg), second (s), kelvin (K) and mole (mol). To describe very large or small amounts, SI adds a prefix, and each prefix is just a power of ten, the same powers you used in Multiplying and Dividing by Powers of 10 and Scientific Notation.
Key idea
A prefix stands for a power of ten: replace it with that power. $2.5\ \text{km} = 2.5 \times 10^{3}\ \text{m} = 2500\ \text{m}$. Converting to a smaller unit gives a bigger number.
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| giga | G | $10^{9}$ | 1 GB |
| mega | M | $10^{6}$ | 1 MW |
| kilo | k | $10^{3}$ | 1 km = 1000 m |
| deci | d | $10^{-1}$ | 1 dL = 0.1 L |
| centi | c | $10^{-2}$ | 1 cm = 0.01 m |
| milli | m | $10^{-3}$ | 1 mg = 0.001 g |
| micro | μ | $10^{-6}$ | 1 μm |
| nano | n | $10^{-9}$ | 1 nm |
Why it works
A prefix is a multiplier glued to a unit. "k" means "times 1000", so a kilometer is 1000 meters, just as a dozen eggs is 12 eggs. When you measure the same length with smaller units, you need more of them: 1 km is 1000 m, and 1 m is 100 cm. So a number grows when its unit shrinks, and the amount itself never changes.
Worked examples
Worked example: Milligrams to grams
Convert $350\ \text{mg}$ to grams.
- Milli means $10^{-3}$, so $350\ \text{mg} = 350 \times 10^{-3}\ \text{g}$.
- $350 \times 10^{-3} = 0.350$
- Grams are bigger than milligrams, so the number got smaller, as it should.
Answer: $0.350\ \text{g}$
Worked example: Between two prefixes
Convert $1.5\ \text{mg}$ to micrograms (μg).
- Go through the base unit: $1.5\ \text{mg} = 1.5 \times 10^{-3}\ \text{g}$.
- $1\ \mu\text{g} = 10^{-6}\ \text{g}$, so divide by $10^{-6}$: $\dfrac{1.5 \times 10^{-3}}{10^{-6}} = 1.5 \times 10^{3}$.
- Micrograms are smaller, so the number is bigger: $1500\ \mu\text{g}$.
Answer: $1500\ \mu\text{g}$
Common mistake
Moving the decimal point the wrong way, as in $2.5\ \text{km} = 0.0025\ \text{m}$, or mixing up milli- ($10^{-3}$) with micro- ($10^{-6}$). Check: a kilometer is a long walk and a meter is a stride, so there must be many meters in 2.5 km. A smaller unit always means a larger number.