Operations with Significant Figures

by Patrick Ford
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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 gonna 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 three 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. So we're gonna write the answers expressing the appropriate number of sig figs. The first one is just a simple addition between two numbers. So if you look at these three rules here, which one does that apply to? Well, it turns out this one actually just applies to if it's just addition or subtraction on Lee. And here's the rule. If you're on Lee just doing addition and subtraction, then you go around the answer to the same number of decimal places as the number with the least number of decimal places. So it's all about the decimal places when you're doing addition, subtraction, so for instance, I've got two decimal places over here, and then I've got four decimal places over here. So you just plug this straight into your calculator and we're gonna round to the number with the least number of decimal places, which is the second one, which is two decimal places. So, for example, if you just plug this into your calculator, you're gonna get 8.85 01 But we have to round it to the second decimal place. So the way we around this is, we just look at the third digit, and if it's five or more, we round it up. But this just rounds to 8.85. And that's the answer. Let's take a look at the second one. The second one. Now we have 5.83. We have subtraction, and we have addition. But even though this is a subtraction and addition, it still falls under the rule off addition and subtraction on Lee. So we're on Lee just going to round to the nearest or so to the, uh, decimal places at the number with the least decimal places. So here we've got three here. We've got one and then here we've got three. So the way you're going to do this is you're always gonna move left to right in your calculator. You're just gonna plug this straight into your calculator exactly as you see it. Because if you try to do this first, like 4.3 plus 0.1 of three and then do the subtraction, you're gonna get the answer wrong. So you always just go from left to right. So if you just plug this straight into your calculator, you're gonna get 1.1 92. But remember, we have to round now to the number with least decimal places, which is just the first one. So if we go ahead and round this now, this second digit over here is a nine. So we rounded up. So this is gonna be 1.2. Let's take a look at C. C now has division and multiplication. So which rule does this apply? Thio, we'll see, will apply to the second rule. If it's if it's multiplication and division Onley, then the rule is we're gonna look and we're going around the answer to the same number of Sig figs or significant figures as the number with the least number of sig figs. So now it's not about the decimal places. It's actually just about the number of significant figures. So, for example, here these are all non zero numbers. So this is, I believe, six. So this is six Sig figs here, whereas this number here remember, we eliminate the leading zeros and then count up. This is four Sig figs and this this last number eliminate the leading zeros. And this is actually to sig Figs. So we're actually going around to the second to the number with the least number of sig figs. That's this one over here and again. Just move left to right in your calculator, just plugging it exactly as you see it. And if you do this, you're gonna get 1.1 or sorry, 1 92 8274 blah, blah, blah. Right. But we just have to round it to the second significant figure. So in this case, it's not about the decimal place. Don't round it to the second decimal place. The second significant figure here is actually the nine. So we're gonna round to this place over here, so this is just gonna be 1.9. And that's our answer Now for this last one here. Now we've got multiplication, and we have addition that are mixed up inside this number. So for this last one for the part D, this actually falls under this rule over here. If it's addition and subtraction and you're mixing it with multiplication or division, then what you have to do is you just use your order of operations, which is Please excuse, my dear Aunt Sally, right pen desk. And you get around the answer to the most number of significant figures. That's the rule. So basically, we're gonna follow our order of operations. Multiplication and division always comes before addition and subtraction. So in this case, you're not gonna move left to right. You're always just gonna follow your order of operations. So in this case, we're gonna do this first and then we're gonna add it to 4.68. And if you do this correctly, where you're gonna get in your calculator is eight point 85085 Sorry, 1067 But remember, Now we have to keep track of all the significant figures. In this case, there is five here, 56 figs. And in this case, we're eliminate the leading. And there's two sig figs here. And then for this number, there are three. So the number with the most amount of Sig figs is actually this one here, So we're gonna keep it to five significant figures. And so we're gonna round this off. And the fifth significant digit here is 12345 So we're gonna round to this place over here. So what we have to do is 8.81 Sorry. 8.8510 And then we look at this number and it's higher than higher than five. So we round it. So we're going around this to seven, and this is actually the answer. Alright, guys, that's it for this one. Let me know if you have any questions.