1.1.2

# SI Prefixes, Standard Form & Converting Units

Test yourself

## Prefixes of Units

Using prefixes before a unit indicates the scale of the value.
For example, 1 nanometre (nm) = 10-9m. 3nm = 3×10-9m.

### Nano (n)

• Multiplies the unit by 10-9.
• This is equivalent to multiplying by 0.000000001.

### Micro (μ)

• Multiplies the unit by 10-6.
• This is equivalent to multiplying by 0.000001.

### Milli (m)

• Multiplies the unit by 10-3.
• This is equivalent to multiplying by 0.001.

### Centi (c)

• Multiplies the unit by 10-2.
• This is equivalent to multiplying by 0.01.

### Kilo (k)

• Multiplies the unit by 103.
• This is equivalent to multiplying by 1000.

### Mega (M)

• Multiplies the unit by 106.
• This is equivalent to multiplying by 1000000.

### Giga (G)

• Multiplies the unit by 109.
• This is equivalent to multiplying by 1000000000.

## Standard Form

Standard form is used to represent very large or very small numbers. In standard form numbers are written in the format: A x 10n where A is a number between 0 and 10 and n is how many places to move the decimal point.

### Standard form examples

• To write 1,000,000 as standard form 1 x 106.
• To write 0.0004 as standard form 4 x 10-4.

## Converting Units

Consider a simple example of how to convert units. Let us say that we want to convert 80 metres (m) to kilometres (km).

### Step one

• The first thing to do is to list the units that you have and the units that you want to convert to.
• In this case, we have units in metres and we want to convert to kilometres.

### Step two

• Next, we need to determine a conversion factor relating metres to kilometres.
• A conversion factor is a ratio expressing how many of one unit are equal to another unit.
• For example, there are 12 inches in one foot, 100 centimetres in one metre, 60 seconds in one minute, and so on.
• In this case, we know that there are 1,000 metres in one kilometre.

### Step three

• Now we can set up our unit conversion.
• We write the units that we have and then multiply them by the conversion factor so that the units cancel out, as shown in the image.
• Note that the unwanted m unit cancels, leaving only the desired km unit.

### Other examples

• You can use this method to convert between any types of unit.
• For example between J and eV or between J and kW/h.