Every measurement carries a unit — metres, grams, seconds. A recipe needs 250 g of flour; a road sign says 40 mph; a bottle holds 1.5 litres. This chapter is about converting between units so numbers can be compared, and about compound measures: quantities built from two units combined, like speed (distance and time) or density (mass and volume).
Converting metric units
The metric system is built on powers of 10, so every conversion is just a multiply or a divide — never anything awkward. Learn the ladder once and it covers length, mass and capacity:
- Length: 10 mm = 1 cm · 100 cm = 1 m · 1000 m = 1 km.
- Mass: 1000 g = 1 kg · 1000 kg = 1 tonne.
- Capacity: 1000 ml = 1 litre.
The direction is the bit to get right: going to a smaller unit you multiply (more of them fit), going to a bigger unit you divide (fewer needed). Think of money: 1 pound = 100 pence, so pounds → pence is ×100, and pence → pounds is ÷100. Units work exactly the same way.
Compound measures: speed
A compound measure combines two different units. Speed combines distance and time, and its unit shows it — km/h means "kilometres per hour". The three quantities are locked together, so any one can be found from the other two:
The formula triangle in the picture is a memory aid: cover the letter you want and read off what is left. Cover D and you see S × T; cover S and you see D over T; cover T and you see D over S.
Density
Density works exactly the same way and tells you how much mass is packed into each unit of volume — why a small lead ball feels far heavier than a big beach ball:
| Measure | Formula | Typical unit |
|---|---|---|
| Speed | distance ÷ time | km/h, m/s |
| Density | mass ÷ volume | g/cm³ |
| Rate of pay | pay ÷ hours | £/hour |
Memory hook: a compound measure is always "this per that", and the slash in the unit (km/h, g/cm³) tells you what to divide by what. To smaller units multiply, to bigger units divide.