Orders of magnitude

Our standard unit of length is the metre, m. This is useful for things of a human scale but less good for measuring very small or very large objects. That is why we use other units that are multiples of metres, for example:

• 1mm (millimetre) = 0.001m
• 1cm (centimetre) = 0.01m
• 1km (kilometre) = 1000m

Each division or multiplication by ten is termed an order of magnitude. For example, there is one order of magnitude between the height of a four-year old child (1m) and the height of an apple tree (10 m).

When considering orders of magnitude the actual length may be approximated, it is the relative difference which is important.

For instance there are three orders of magnitude between a fly (about 1 cm) and a truck (10 m) as the truck is $$1000$$ $$(10 \times 10 \times 10)= 10^{3}$$ times longer than the fly.

Question

By how many orders of magnitude is the Earth (diameter approx. 12 000 km) larger than a large garden pea (1.0 cm diameter)

Converting both to metres:

$Pea=0.01m=10^{-2}m$

$Earth= 1.2 \times 10^{7}m$

The Earth is approx $$10^{7}\div 10^{-2}= 10^{9}$$ or $$1,000,000,000$$ times bigger which is $$9$$ orders of magnitude greater.