Hey, guys. So we've seen how to count up the number of significant figures in our numbers. But a lot of times, you're going to have to do math with sig figs in your problems, like addition, subtraction, multiplication, and division. And so when you're doing math to calculate values, there are 3 additional rules to determine the number of significant figures of your final answer. So I've got these three rules down here, but let's just jump straight into the example so I can show you how they work. So let's check it out. We're going to write the answers expressing the appropriate number of sig figs. The first one is just a simple addition between two numbers.

If you look at these three rules here, which one does it apply to? Well, it turns out this one actually just applies to if it's just addition or subtraction only. Here's the rule: If you're only just doing addition and subtraction, then you're going to round the answer to the same number of decimal places as the number with the least number of decimal places. It's all about the decimal places when you're doing addition and subtraction. For instance, I've got 2 decimal places over here, and then I've got 4 decimal places over here. Plug this straight into your calculator, and we're going to round to the number with the least number of decimal places, which is the second one, which is 2 decimal places. For example, if you plug this into your calculator, you're going to get 8.8501, but we have to round it to the second decimal place. Look at the third digit, if it's 5 or more, we round it up. This rounds to 8.85, and that's the answer.

Let's take a look at the second one. We have 5.83, we have subtraction, and we have addition. But even though this is subtraction and addition, it still falls under the rule of addition and subtraction only. We're only going to round to the decimal places of the number with the least decimal places. Here we've got 3. Here we've got 1. And then here we've got 3. You're going to move from left to right in your calculator. Plug this straight into your calculator exactly as you see it. If you try to do this first, like 4.3 + 103 and then do subtraction, you will get the answer wrong. Always go from left to right. If you plug this into your calculator, you're going to get 1.192. Remember, we have to round now to the number with the least decimal places, which is just the first one. If we round this, now the second digit is a 9, so we round it up. This will be 1.2.

Let's take a look at example C. This one has division and multiplication. This applies to the second rule: Multiplication and division only. The rule is we're going to round the answer to the same number of significant figures as the number with the least number of significant figures. It's not about the decimal places, it's about the number of significant figures. Here, these are all non-zero numbers. This is 6 significant figures. This number, eliminate the leading zeros and count up, has 4 significant figures, and this last number, eliminate the leading zeros, has 2 significant figures. We're going to round to the number with the least number of significant figures, which is this one with 2. Move from left to right in your calculator and plug it in exactly how you see it. You're going to get 1.928274 blah blah blah. But we just have to round it to the second significant figure. It's not about the decimal place. The second significant figure here is actually the 9, so we're going to round to this place. This will be 1.9, and that's our answer.

Now for the last one here, we've got multiplication and addition mixed up inside this number. This falls under the rule of mixing addition and subtraction with multiplication or division. You round the answer to the highest number of significant figures, following the order of operations. Multiplication and division always come before addition and subtraction. If you do this correctly, what you'll get in your calculator is 8.851067. We have to keep track of all the significant figures: 5 here, 2 here, after eliminating the leading zeros, and 3 for this number. The number with the most significant figures is actually this one, so we're going to round it to 5 significant figures. The fifth significant digit is here, so we round this. Looking at the digit beyond our rounding digit, which is higher than 5, we round it up. This makes it 8.85107. And this is actually the answer.

Alright, guys. That's it for this one. Let me know if you have any questions.