Unit Conversions Quiz

In science, we use standardised SI units to make measurements by different people comparable without conversion.

For example, we use degrees celsius (˚C) in calculations about temperature and watts (W) in power calculations.

We also use a standard system of larger units that use a prefix and a multiplier to make the numbers smaller or larger and easier to work with.

For example, instead of using Joules to represent very large amounts of energy, we can add a prefix such as kilo, mega or tera to represent them in an easier way for us to work with.

Each of these prefixes is a standardised unit, each 1000x apart. The following table shows the most common prefixes and their relationship to each other. The table also shows how this works using grams (g) as an example.

Before you perform a calculation using a formula in physics, you should first change the units to the correct ones. Usually, this involves converting the number to remove the prefix, except in the case of kilograms, which is the unit to be used in calculations.

The table below shows some of the important units to use.

It is important to note that there are exceptions to this system. In calculations with time, for example, you should use seconds. As you will already know, time has its own system of units – minutes, hours, days etc.

Temperature also does not usually observe the system of using prefixes.

Example 1: mm to m (single step)

To go from mm to m you need to divide the number by 1000 because there is one step between m and mm – there are 1000 mm in 1 m. So if we have 17,000mm, we divide by 1000 to get 17m.

Example 2: kJ to J (single step)

To go from kJ to J you need to multiply by 1000 because there is one step between kJ and J – there are 1000 J in 1 kJ. So if we have 3 kJ, we multiply by 1000 to get 3000 J.

Example 3: TJ to J (multi step)

To go from MJ to J you need to multiply by 1000 twice because there are two steps between MJ and J – there are 1,000,000 J (1 million) in a MJ. So if we have 8.5 MJ, we multiply by 1000 and then 1000 again to get 8,500,000 J.

Alternatively, you can use index powers to achieve this more cleanly. 1000² = 1,000,000 or 1000 x 1000. The same applies for more steps, so if we need to go up three steps from pm to mm we can divide by 1000³. E.g. 28,000,000 pm x 1000³ = 0.028 mm.

Remember, when using these very large and small numbers we can also use standard form. Learn more about standard form soon with our quiz on this topic that will be available in Fundamentals in Science soon.

Centimetres are actually sub-units which don’t fit into the system of prefixes well. There are 100 centimetres in 1 metre (cent is 100 in French).

There are also centilitres and other units you might see occasionally, these are all the same as cm in terms of their relationships with larger and smaller units.

Example – convert from cm to km:

First, convert to m by dividing by 100 then divide by 1000 as normal.