Convert between metric units of length - Mixed conversions
Theory
A mixed conversion crosses more than one step of the unit ladder, so the factors multiply together. Millimetres to metres uses \(10 \times 100 = 1000\). Smaller unit multiplies; larger unit divides.
The length units form a ladder: mm, cm, m, km, with \(10\) mm in a cm, \(100\) cm in a m and \(1000\) m in a km.
To cross two steps at once, use the combined factor. For example mm to m is \(10 \times 100 = 1000\). Going to a smaller unit multiplies; going to a larger unit divides.
For a compound length such as \(3\) m \(5\) cm, change each part to the same unit first, then combine.
Each rung has its own factor; crossing two rungs multiplies them.
| Steps crossed | Factor |
|---|---|
| mm ↔ cm | \(10\) |
| cm ↔ m | \(100\) |
| mm ↔ m | \(1000\) |
| m ↔ km | \(1000\) |
How to do a mixed conversion
- Count the steps between the two units on the ladder.
- Combine the factors by multiplying them together.
- Multiply for a smaller unit, or divide for a larger unit.
Larger unit, two steps, so divide by \(1000\): \(4500 \div 1000 = 4.5\).
The answer is 4.5 m.
Smaller unit, two steps, so multiply by \(1000\): \(0.4 \times 1000 = 400\).
The answer is 400 mm.
Change to cm, then to mm.
\(3 \times 100 = 300\), then \(300 + 5 = 305\), then \(305 \times 10 = 3050\).
The answer is 3050 mm.
Larger unit, so divide by \(1000\): \(2700 \div 1000 = 2.7\).
The answer is 2.7 m.
Common pitfalls
Frequently asked questions
How do you convert millimetres to metres?
Divide by \(1000\), because two steps are crossed: \(10 \times 100 = 1000\). For example \(4500\text{ mm} = 4.5\text{ m}\).
Why is the factor 1000 and not 100?
Millimetres to metres crosses two steps of the ladder, mm to cm and cm to m, so the factors \(10\) and \(100\) multiply to \(1000\).
How do you write 3 m 5 cm in millimetres?
Change the metres to centimetres: \(3 \times 100 = 300\), add the \(5\) to get \(305\) cm, then multiply by \(10\) to get \(3050\) mm.
How do you handle a compound length?
Change each part to the same unit first, then add them together before converting to the unit asked for.