 In this video we'll look at unit conversions, that is, how to convert a measurement taken in one kind of unit into another kind of unit. For instance, a recipe tells you that you need 1.35 kilograms of flour, but your scales only measure in grams. So you need to work out how many grams are equivalent to 1.35 kilos. Now you're familiar enough with this kind of conversion that you can probably do it in your head. But let me show you a formal way of doing the conversion so that when, for instance, you're asked to convert milliseconds into weeks, you'll have something to fall back on. I'm going to set this out by writing my quantities as fractions. You'll see why in a second. What I know is the 1.35 kilograms of flour, so I'm going to put that over a denominator of 1 so that its value doesn't change. Now to change this into grams, I need to know the conversion factor between kilograms and grams. So I know that 1 kilogram is equivalent to 1,000 grams. This is the conversion factor. I can write this as 1 kilogram over 1,000 grams or as 1,000 grams over 1 kilogram. Either way, the quantity on the top is exactly the same as the quantity on the bottom. It's just that they're expressed in different units. So I want to apply this conversion factor to my mass. But the thing that sometimes trips people up in these calculations is whether to multiply by 1,000 or divide by 1,000. Which way up should the conversion factor go? So here's the trick. You can use the units to guide you. You know that your original mass is in kilograms and you want your final mass to be in grams. So your aim is to arrange the fraction so that the kilograms cancel out. To do this, you need to write this conversion factor with the kilograms on the bottom. Now you know that in fractions anything that's both on the top and the bottom will cancel out because dividing something by itself just gives you 1. So here we can cancel the kilograms out. And you can see now that the only unit left is the grams. Now to do the calculation, we're simply multiplying fractions. So we multiply the numerators together and we multiply the denominators together. And then we divide the numerator by the denominator. And so you see that the answer is 1,350 grams as you would have predicted.