Measurement units
Units of measurement are used to indicate how large a quantity is. When we measure length, mass, time or other quantities, we use fixed units so that the results can be compared and understood by everyone.
The International System of Units (SI)
Most countries today use the International System of Units, abbreviated SI (from French Système International d’Unités). The system is based on seven fundamental units from which all others can be derived.
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
From these fundamental units, derived units can be formed.
For example, the unit of speed is \( \large \frac{\text{metre}}{\text{second}} = \text{m/s} \), and the unit of area is \( \large \text{m}^2 \).
SI prefixes
Instead of writing very large or very small numbers, prefixes are used to show how many times the unit should be multiplied or divided by ten. For example, kilo means one thousand, while milli means one thousandth.
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| kilo | k | \( \large 10^3 = 1000 \) | 1 km = 1000 m |
| hecto | h | \( \large 10^2 = 100 \) | 1 hg = 100 g |
| deca | da | \( \large 10^1 = 10 \) | 1 dam = 10 m |
| deci | d | \( \large 10^{-1} = 0.1 \) | 1 dm = 0.1 m |
| centi | c | \( \large 10^{-2} = 0.01 \) | 1 cm = 0.01 m |
| milli | m | \( \large 10^{-3} = 0.001 \) | 1 mm = 0.001 m |
Conversion between prefixes
When converting between two units with different prefixes, the decimal point is moved according to how many powers of ten the difference represents. For example:
$$ \large 1\ \text{km} = 1000\ \text{m} = 100\,000\ \text{cm} $$
In the same way, one can convert between litres, grams, metres and many other units simply by knowing the value of the prefixes.