4.1 Linear and logarithmic scales

You will note that the scale on the graph is logarithmic. That is, each increment represents a 10-fold change in size (as we saw in Chapter 3, a 10-fold change in size is known as an order of magnitude). This kind of scale is useful to display widely different values – in this case the graph covers 11 orders of magnitude (or from 1 to 100 billion). This would be roughly the equivalent to the difference in the diameter of a grain of sand (0.05 mm) to the diameter of the Earth (12.7 km or 12,700,000,000 mm). On a linear scale the very small values would be bunched up together and be hard to distinguish. You will also note that rather than using the one unit, say metres (m), prefixes have been used to avoid either very large or very small numbers.

• The prefix m (milli) denotes 1/1,000th (10^–3) of the base unit – for example, there are 1,000 mm in a metre
• µ (micro) denotes 10^–6 × the base unit
• n (nano) denotes 10^–9 × the base unit

Some prefixes you will be familiar with while some you may need to memorise. It is important to be able to quickly and confidently convert between these units.