Arithmetic Operations
Unit Conversions Using Arithmetic
Every unit conversion is just a multiplication or division by the right conversion factor. Learn the factor and the calculation becomes trivial.
Because the metric system is built entirely on powers of ten, converting between its units never requires anything more complicated than shifting a decimal point – multiplying or dividing by 10, 100, or 1,000. This is precisely the feature the French Revolutionary scientists were chasing when they designed the metric system in the 1790s: a measurement system where the everyday arithmetic of trade, science, and construction stays as simple as possible. Anyone measuring out flooring, fencing, or fabric for a DIY project relies on exactly this arithmetic every time they convert a shop's metre measurements into the centimetres needed to check a fit.
Length
| Conversion | Operation |
|---|---|
| km → m | × 1,000 |
| m → cm | × 100 |
| cm → mm | × 10 |
| m → km | ÷ 1,000 |
Mass
| Conversion | Operation |
|---|---|
| kg → g | × 1,000 |
| g → mg | × 1,000 |
| g → kg | ÷ 1,000 |
Capacity
| Conversion | Operation |
|---|---|
| litre → ml | × 1,000 |
| ml → litre | ÷ 1,000 |
Worked Examples
3.6 × 1,000 = 3,600 m
2,500 ÷ 1,000 = 2.5 kg
Imperial Conversions
| Imperial | Metric (approx.) |
|---|---|
| 1 mile | 1.609 km |
| 1 inch | 2.54 cm |
| 1 pound (lb) | 454 g |
| 1 pint | 568 ml |
Key Takeaways
- Smaller to larger unit: divide.
- Larger to smaller unit: multiply.
- Memorise the key conversion factors: 1000 (km/m, kg/g), 100 (m/cm), 10 (cm/mm).