So now we're going to see how significant figures can be incorporated in different calculations that we'll be exposed to in chemistry. Now we're going to start out with multiplication and division. We're going to say when either multiplying or dividing different numbers, the final answer will contain the least significant figures. And if we take a look at this example, it says, perform the following calculation to the right number of sig figs. Here we have 3 values that are being multiplied together. We have 3.16 times 0.003027 times 5.7 times 10^{-3}. We just said that when you're multiplying or dividing its least number of sig figs for your final answer, so we need to determine the number of sig figs for each value. From our topic on significant figures, we know that if we have a decimal point, which all of them do, we move from left to right. Now remember, we're going to start counting once you get to our first non-zero number. Here, 3 is our first non-zero number, and once we start counting, we count all the way into the end. So 1, 2, 3, this has 3 sig figs. For the next one, skip, skip, skip, our first non-zero is this 3. 1, 2, 3, 4. This has 4 sig figs. And then finally we have 5.7 times 10^{-3} written in scientific notation. Remember, when it's written in scientific notation, just focus on the coefficient. We're going to say our first non-zero number is this 5, and once we start counting, we count all the way into the end. So one, 2. This has 2 sig figs.

Now based on our sig figs of 3, 4, and 2, we have to go with the least number of significant figures. That means our answer at the end can only have 2 significant figures. So when we first get our answer, what we see initially is 5.4522324 times 10^{-5}. We want 2 sig figs here. That 4 that we have though, we look to the right of it and see if we either keep it as 4 or we round up. Next to it, we have this long string of numbers, and we have a 5 there. Because that number is 5, that means we have to round up. So the 5.4 becomes now 5.5, and then times 10^{-5}. This represents our answer, which has the least number of significant figures based on the initial values given. We were given these three numbers initially and the one with the least number of sig figs was the one written in scientific notation. So that tells me that my final answer has to have that number of significant figures.

Now that we've looked at multiplication and division, let's go on to our next video and let's see what happens when we incorporate addition and subtraction.