by Jules Bruno

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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