Why a shared system?
In 1999, NASA lost the Mars Climate Orbiter. One team had used imperial units (pound-force seconds) while another expected metric units (newton-seconds). The spacecraft flew too close to Mars and was destroyed. Clear, shared units matter.
Scientists everywhere use the metric system, in its modern form called the SI (Système international d’unités). Because it’s based on powers of ten, changing units is just a matter of moving the decimal point.
SI base units
Each base unit measures one basic quantity.
| Quantity | Base unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric current | ampere | A |
| Amount of substance | mole | mol |
| Light intensity | candela | cd |
Other units, called derived units, are built from these. Speed is metres per second (m/s), and density is grams per cubic centimetre (g/cm³).
Metric prefixes
A prefix tells you how many times bigger or smaller a unit is than the base unit.
| Prefix | Symbol | Meaning | Example |
|---|---|---|---|
| kilo- | k | 1000 | 1 km = 1000 m |
| hecto- | h | 100 | 1 hm = 100 m |
| deca- | da | 10 | 1 dam = 10 m |
| (base) | 1 | 1 m | |
| deci- | d | 0.1 | 1 dm = 0.1 m |
| centi- | c | 0.01 | 1 cm = 0.01 m |
| milli- | m | 0.001 | 1 mm = 0.001 m |
| micro- | µ | 0.000 001 | 1 µm = 0.000 001 m |
A memory trick for kilo to milli: "King Henry Died By Drinking Chocolate Milk."
Converting by moving the decimal
Each step on the kilo-to-milli ladder is a factor of 10.
- Going to a smaller unit: multiply (move the decimal right).
- Going to a larger unit: divide (move the decimal left).
Examples:
- 3.5 km to m: 3 steps smaller, so 3.5 × 1000 = 3500 m
- 250 mL to L: 3 steps larger, so 250 ÷ 1000 = 0.250 L
- 47 mm to cm: 1 step larger, so 4.7 cm
Dimensional analysis
For trickier conversions, use dimensional analysis. Multiply by a conversion factor, a fraction equal to 1, arranged so the unit you don’t want cancels out.
Convert 72 km/h to m/s:
72 km/h × (1000 m / 1 km) × (1 h / 3600 s) = 20 m/s
The km cancels with km, and h cancels with h, leaving m/s.
Scientific notation
Scientists often deal with huge or tiny numbers. Scientific notation writes them as a number from 1 to 10 times a power of 10.
- The distance to the Sun: 150 000 000 km = 1.5 × 10⁸ km
- The width of a bacterium: 0.000 002 m = 2 × 10⁻⁶ m
A positive exponent means a big number; a negative exponent means a small one.
Volume and mass connections
The metric system links units neatly:
- 1 mL = 1 cm³
- 1 L of water has a mass of about 1 kg
- 1 mL of water has a mass of about 1 g
Common mistakes
- Moving the decimal the wrong way. Ask: should the number get bigger or smaller?
- Mixing up m (milli) and M (mega). Case matters.
- Dropping units in the middle of a calculation.
Try it yourself
- Convert 2.4 m to cm.
- Convert 5600 g to kg.
- Convert 0.75 L to mL.
- Use dimensional analysis to convert 15 m/s to km/h.
- Write 0.00045 m in scientific notation.
(Answers: 240 cm; 5.6 kg; 750 mL; 54 km/h; 4.5 × 10⁻⁴ m)
Quick recap
- The SI is the shared measurement system of science.
- Base units include the metre, kilogram, second and kelvin.
- Prefixes show powers of ten; converting moves the decimal point.
- Dimensional analysis uses conversion factors so units cancel.
- Scientific notation keeps very large and small numbers manageable.