Standard form

This is a convenient way to represent large and small numbers. It is often called scientific notation as scientists are constantly using extremely large and extremely small numbers. For example, physicists investigating atomic structure measure very small quantities such 9.1 × \(10^{-31}\) kg the approximate mass of an electron.

On the other hand, space scientists talk about the distance travelled by light in one year which is 9.46 × \(10^{15}\) m.

Metric names

Metric names for some powers of 10 are part of the standard system:

The prefix 'kilo' corresponds to the power \(10^3\).

The prefix 'milli' corresponds to the power \(10^{-3}\).

So we have the units of mass and volume:

• 1 kilogram = \(10^3\) grams, 1 kilometre = \(10^3\) metres, 1 kilolitre = \(10^3\) litres.
• 1 milligram = \(10^{-3}\) grams, 1 millimetre = \(10^{-3}\) metres, 1 millilitre = \(10^{-3}\) litres.

This system is in stark contrast to other systems such as the imperial system, where larger and smaller units were not standardised and named as the result of some convention. For example, in the imperial measurement system,

1 league \(\approx\) 3 miles.

This was originally the distance a person could walk in 1 hour.