# 5.1 Converting between SI units

The following section provides a systematic approach you can use to convert between SI units. You will gain confidence with these kinds of conversions only through practice, and you will need to memorise the unit prefixes and what conversion factor they represent.

When converting to or from a base unit you need to determine the conversion factor. A way to do this is to use 1 for the prefixed unit and a power of 10 in front of the base unit.

#### Example 1

How many mg are in 1 g?

1 mg = 10^{–3} g

Multiply both sides by 1,000 (10^{3})

Therefore, 1,000 mg = 1 g

#### Example 2

Convert 10 µg to g

10 µg = 10 × 10^{–6} g

#### Example 3

What about converting from one prefix to another? You can do this as a two-step process by going through the base unit and using two conversion factors.

How many ng are in 1 kg?

**Step 1:** 1 ng = 10^{–9} g

Therefore, 10^{9} ng = 1 g

**Step 2:** 1 kg = 10^{3} g

Therefore, number of ng in 1 kg = 10^{9} × 10^{3} = 10^{12} ng

Note that when multiplying numbers with the same base, add the exponents;

the general rule is a^{b} × a^{c} = a^{b+c}

### Rules for using SI units

The SI is used because it is precise, but it has also developed some conventions to avoid ambiguity. Below are the rules you should follow when using SI units. However, you will come across many examples – often in popular media, but also unfortunately even in some textbooks or peer-reviewed publications – where these rules are broken due to ignorance or carelessness!

- Never pluralise units. This can cause confusion, as kms does not mean kilometres but would be interpreted as km multiplied by s.
- Never use a full stop after unit abbreviations unless it is the end of a sentence.
- The unit (plus prefix) should be separated from the unit by a space (e.g. 10.3 µl).
- Do not separate prefixes from the unit by a space. (e.g. 10 micrometres should written 10 µm not 10 µ m)
- When you combine units, separate them by a space (e.g., 10 mg l
^{–1}). This example means ‘10 milligrams per litre’. You can use –1 or use a slash (/) for per (e.g. 10 mg/l). Do not write ‘per’. - Only use one prefix in front of a unit.
- A unit named after a famous person, such the joule (named after the English physicist James Prescott Joule, 1818–1889), is written in lowercase but when abbreviated is written in uppercase (J).