Key concepts of physics - EdexcelMultiple and sub-multiples of units

Sometimes a measurement, using the standard SI unit, will give a very large or very small number that is inconvenient to write out in full. For example, the distance from the Sun to Pluto varies from 4,400,000,000,000 m to 7,300,000,000,000 m.

Standard form

Mathematicians have a system for writing large numbers in a shortened way called standard form.

This involves writing the value digits of the number as a number between 1 and 10, and then writing that number multiplied by a power of ten to expand it back to the full number represented.

For example, the distances from the Sun to Pluto range from:

4,400,000,000,000 m = 4.4 × 10¹² m

to

7,300,000,000,000 m = 7.3 × 10¹² m

Unit prefixes

Another system to reduce the problem of very long numerical measurements uses a standard set of abbreviations to cut down the numbers that need to be written. For example, 1,000 metres is a kilometre, so instead of '1,000 m' scientists write '1 km'.

Using prefixes, the distances from the Sun to Pluto range from:

4,400,000,000,000 m = 4.4 × 10¹² m = 4.4 terametres = 4.4 Tm

to

7,300,000,000,000 m = 7.3 × 10¹² m = 7.3 terametres = 7.3 Tm