 Okay, now what happens when we multiply values? Then we can follow exactly the same process again. And we expand out the bracket. We're going to have four terms. We're going to have A times B, which is going to cancel with that A times B. We're going to get terms we have an error times the other value. And then we're going to have the term where we have the two errors multiplied together. And what we normally do is we normally ignore the term when we have the two errors multiplied together because we assume they're both quite small, or else most of our approximations are going to get a bit loose anyway. And so when we multiply two small numbers, we get a tiny number. And so we're going to end up with just those two cross terms. And a good way to remember that is to divide both sides by Y. So if we have our error in Y divided by Y, that's going to be what we just worked out, divided by our definition of Y in the first place. And so we've got two terms here. And so when we have the first term, the A's are going to cancel. The B's are going to cancel. And this quantity where you divide the uncertainty by the quantity itself is called the relative uncertainty. Whereas the error just by itself is called the absolute uncertainty. And the rule is very simple. If you're multiplying things, you add the relative uncertainties. And a similar argument tells us the same thing works for division. Okay, let's do a couple of examples. So let's suppose that we have a box of apples. We've got 100 apples and we weigh them. And we figure out that their mass together is 10.3 plus or minus 0.2 kilograms. So how much does one apple weigh? It's going to have mass. Well, there's 100 apples. We divide by 100. So we're going to get a hundredth of our average and we're also going to get a hundredth of our uncertainty. And that's the mass of one apple. Now, suppose we wanted to know how much area the box has on one side. And we measured its height and its width. And if we measured some values for the width and the height with a particular uncertainty, then it's easy enough to get the average area. We simply multiply our width by our height. But what do we do for the uncertainty? Remember, we have to add the relative uncertainty. So the relative uncertainty in this quantity is 1 centimeter divided by 120 centimeters, which is 0.8 percent. And the relative uncertainty in this is 2 centimeters divided by 23 centimeters, which is a lot larger, which is 9 percent. So remember, we have to add the relative uncertainties when we're multiplying two numbers. And so we add 9 percent and 0.8 percent, which rounded gives us 10 percent. And so our error here is going to be 276 square centimeters. But remember, we can't quote all these extra significant figures down here. And if we're going to have an error that big, which is going to round to 300, then there's no point quoting this number either. So the way we'd quote that properly is like that. So we've got the right number of significant figures in both our uncertainty and our final result.