 Okay, let's do some more examples so that you can get the hang of how this works. Let's convert 456,000 millimetres into kilometres. First put our known quantity over 1 to make it a fraction. Now I don't know the conversion factor that directly takes me from millimetres to kilometres off the top of my head, but that's okay because we can do this in two steps. First let's convert the millimetres into metres. I know there are 1,000 millimetres in a metre and I want to cancel out the millimetres so I'm going to put the conversion factor this way around with the millimetres on the bottom. Then the millimetres cancel and I'm left with units in metres. Now I just need to convert the metres into kilometres and I know that there are 1,000 metres in one kilometre so I'm going to do much the same thing again. Cancel out the metres and I'm left with kilometres. Now I just have to run through the calculations. I multiply through the top and then the bottom and then I divide the top by the bottom. Now I should point out that you can do this in one go on your calculator rather than treating the top and the bottom separately, but there is a trap for the unwary. Let's run through and see what happens if we do this, and this is not our answer. What's happened is that the calculator which follows order of operations has divided 456,000 by 1,000 but has then multiplied by 1,000 which is really what you instructed it to do. What we want it to do is to divide 456,000 by brackets 1000 times 1000. So that's what we need to put in. We use brackets to encapsulate the bottom of the fraction. Always make sure you do this.