 ## General Chemistry

Learn the toughest concepts covered in Chemistry with step-by-step video tutorials and practice problems by world-class tutors

1. Intro to General Chemistry

# Significant Figures: In Calculations

Significant Figures are often involved in chemical calculations.

Significant Figures In Calculations
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## Significant Figures Calculations Concept 1 3m
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So now we're gonna see how significant figures can be incorporated in different calculations that will be exposed to in chemistry. Now we're gonna start out with multiplication and division. We're gonna 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 performed the following calculation to the right number of Sig figs. Here we have three values that are being multiplied. Together we have 3.16 times 0.30 to 7 times 5.7 times 10 to the negative three. 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 sick fix for each value from our topic on significant figures. We know that if we have a decimal point, which all of them dio we move from left to right. Now remember, we're going to start counting once you get to our first non zero number. Here three is our first non zero number, and once we start counting, we count all the way into the end. So 123 This has three sick fix for the next one. Skip, Skip, Skip our first non zero is this three? 1234 This has four sig figs. And then finally, we have 5.7 times 10 to the negative three written scientific notation. Remember, when it's written in scientific notation, just focus on the coefficient. We're going to say I'm not our first non zero number is this five? And once we start counting, we count all the way into the end. So one to this has to sick things. Now, based on our sig figs of 34 and two, we have to go with the least number of significant figures. That means our answer at the end can only have two significant figures. So when we first get our answer, what we see initially is 5.452 to to four times 10 to the negative five. We want to sick fix here that for that we have, though we look to the right of it and see if we either keep it is four or we round up next to it. We have this long string of numbers and we have a five there because that number is five. That means we have to round up. So the 54 becomes now and then times 10 to the negative five. 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 scientific notation. So that tells me that my final answer has toe 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.
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## Significant Figures Calculations Concept 2 1m
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now, when either adding, subtracting different numbers. The final answer will contain the least decimal places. If we take a look at this example, it says performed the following calculation to the right number of sick things. Now, if our answer is based on the least number of decimal places, that's gonna have a direct impact on the number of significant figures. If we take a look here, it says we have four or 2.9 minus to 12.2 plus 2.671 If we look at these values, this one has two decimal places. This one here has one decimal place, and this one here has three decimal places. Based on that, we're going with the least number of decimal places are answer can only have one decimal place at the end. When we punch all this in, we get 1 92 561 We can only have one decimal place to the right of that five. There's a six there. That means we have to round up. So this is 1 82 6 as our final answer. And if you wanted to talk about the number of sick figs you'd move from left to right. Our first non zero number is this one and counting all the way through, we'd have four sig figs at the end. By following this least number of decimal places, it has a direct impact on the number of sick figs. In our final answer up to this point, we've kept multiplication and division separate from addition and subtraction. But what happens when you mix them together to find out what to do? Click on the next video.
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## Significant Figures Calculations Concept 3 5m
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Problem

Perform the following calculation to the right number of sig figs:
[(1.7 × 106) ÷ (2.63 × 105)] + 6.96

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What answer should be reported, with the correct number of significant figures, for the following calculation?
[(42.00 − 40.914) ⋅ (25.739 − 25.729)] / [(11.50⋅1.001) + (0.00710 ⋅ 700.)] 