Prefixes and conversions

Measuring the thickness of a hair in metres gives 0,00007 m. Measuring the distance between the Earth and the Sun gives 150 000 000 000 m. Neither is legible.

Prefixes solve this problem: they multiply the unit by a power of 10.

Prefixes you need to know

Prefix	Symbol	Factor
giga	G	10^9
mega	M	10^6
kilo	k	10^3
—	—	1
centi	c	10^-2
milli	m	10^-3
micro	u	10^-6
nano	n	10^-9

A hair is therefore 70 um (70 micrometres), which is much easier to read and compare .

Converting without making mistakes

The question to ask is always the same: should the number get bigger or smaller?

2,5 km  ->  m

A metre is smaller than a kilometre, so you need more of them: the number gets bigger.

2,5 km  =  2,5 x 1000  =  2500 m

The other way round:

450 g  ->  kg

A kilogram is larger than a gram, so you need fewer of them: the number decreases.

450 g  =  450 : 1000  =  0,45 kg

This ‘more or less’ question prevents 90 per cent of conversion errors. If you get 0.0025 m for 2.5 km, you can see straight away that this is absurd: 2.5 km cannot be less than one centimetre.

The trap of square units

1 m   =  100 cm
1 m^2 =  10 000 cm^2      (and not 100)

A square with sides of one metre contains 100 × 100 = 10,000 squares of one centimetre. When the unit is a square, the conversion factor is also a square. For volumes, it’s a cube: 1 m^3 = 1 000 000 cm^3.