 Here, we're going to look at approximation and estimation. A skill that will be required for this is rounding. So if you need a refresher, check out our video here. An approximation is anything that is similar but not exactly the same as something else. For example, if you were to say a 57 minute journey would take about an hour, you would be approximating. A value can be approximated by rounding. Usually, to a value that is easier to work with. Be aware, for approximation questions, you are rarely allowed a calculator. A good rule of thumb for approximating is to round to a position that is one or two positions above the lowest position of the original value. Let's see an example of this rule in action. Say you are purchasing something that's £49. The lowest positional value is 9 in the units column. Using our rule, we round to one position higher which gives us £50. Because 50 is a multiple of 10, it's a much easier value to work with, so our approximation is £50. Have a go at approximating these questions, rounding it up just one place value. Pause and have a try. How did you do? If we look at 6.3, its lowest positional value is 3 in the tenths column, so we round it up one position to just 6. For 18.8, the lowest positional value is 8 in the tenths column, so we would round up giving us an approximation of 19. However, if we add some context, let's say you are going on a journey that is 18.8 kilometres. You are trying to calculate the time it will take and are happy to approximate. You know you can travel at 20 kilometres per hour. Whilst it's certainly possible to calculate time from these values, looking at your approximated distance, 19 kilometres, it is still not the easiest value to work with. At this stage, we can therefore approximate a second time. What do you think that would give us? If we look at the 9 as the lowest possible value positionally, it would round upwards, making the 10 a 20. Now if we look at our values, we have a distance of 20 kilometres, a speed of 20 kilometres per hour, and using distance over speed, we get a time of 1 hour. The exact value would be 0.94, which is 56 minutes and 24 seconds, so our approximation is not far off. Another term you might see is estimate. For example, this question here. To estimate an answer, we use approximation to make the values all nice and easy to use. Use approximating on this question and see if you can find a good estimate. Try for an integer answer without using a calculator. Let's see how you did. We can look at 5.9 and approximate this to 6. 42.4 has a lowest positional value of 4, so we'd round initially to 42. Here we could round to 40, as it's usually an easier value to work with, but we don't know the full context of the question yet, so it's worth waiting to see. Our 11.7 can become 12, again we will leave this just for now, and 4.8 become 5. Subtracting 6 and 42 gives us 48, and subtracting 5 from 12 gives us 7. So far, our approximations have given us 48 divided by 7. Now if we look carefully at our question, we are dividing by 7. To get an integer answer, we would need a multiple of 7 for our integer. Fortunately, 49 is right next to 48, so we can say 48 is approximately 49. This gives us 49 divided by 7, which equals 7, an integer value. We hope you found this helpful.