Durham College - Unit conversions - Example #5 - Sals tutorial

The question here is to convert a length of 6 feet and 3 and a quarter inches into metres. In this example, a single quantity is being measured using two different imperial units - feet and inches. You can think of it as an addition of 6 feet plus 3 and a quarter inches. The simplest way to answer this question is to convert the 6 feet to metres, then convert the three and a quarter inches to metres separately, and then add those two results together. In order to accomplish this, we need conversion factors to convert feet to metres, and also to convert inches to metres. So if I look this up on Google, I can find out that 1 metre is the same as 3.28 feet and also 1 metre is equal to 39.36 inches. So the first step is to take the 6 feet and convert it into metres. To do that, I can multiply it by a conversion factor of 1 metre over 3.28 feet or 3.28 feet over 1 metre. I'll need to choose the one with feet on the bottom so that feet will cancel out with the original amount and leave metres on the top. So the result with be 6 feet times 1 metre over 3.28 feet. The feet cancel, leaving metres as the only unit, and 6 times 1 divided 3.28 gives 1.83 metres. So 6 feet is the same as 1.83 metres. We're done step 1. The next step is convert 3 and a quarter inches to metres. But first I need to change this mixed fraction - you see, 3 and a quarter - into a decimal. 1 divided by 4 is 0.25 so three plus a quarter should be 3 plus .25 which is 3.25. And here is all the work for that. If you find this confusing, you may need to review some of the rules for fractions. But the point of it is to change the 3 and a quarter inches to 3.25 inches because that will make it easier to work with. So, now I have a length of 3.25 inches, and I need to multiply that by something to change it into metres. So using the unit relation I found earlier, I can either multiply it by 1 metre over 39.36 inches or 39.36 inches over 1 metre. In order to make the inches cancel out, I need to multiply by the one that had inches on the bottom. So multiply it by the conversion factor: 1 metre over 39.36 inches. When I multiply 3.25 inches by that, the inches cancel, and the result is 3.28 times 1 over 39.36, which is 0.083 and the only unit left is metres. So now I know that 3.25 inches is the same as 0.083 metres, and all I have to do is add the two parts together. 1.83 metres plus 0.083 metres is 1.913 metres. And that's it! That's the answer! So now I know that 3 feet 3 and a quarter inches is the same as 1.913 metres. So now ask yourself "Does this answer looks right? Does it make sense? Is there a way you can check it?" All I did in the process was divide up the 6 feet 3 and a quarter inches into 6 feet plus 3 and a quarter inches, which I changed to 3.25, then converted them both to metres and added them together to make the total again. So there's nothing wrong with my method. You can just ask yourself "well, how long of a distance is 6 feet 3 and a quarter? Does that sound like about the same 1.9?"