Significant Figures Calculations Concept 3

Jules Bruno
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Now we're dealing with mixed operations, but we have a combination of multiplication, division, subtraction or addition. We're gonna say when dealing with this mixture off multiplication division, addition and subtraction, we must follow the order of operations to help us remember, The order of operations will use pen dis, which stands for parentheses. So what's in parentheses is done first exponents or powers. Then we have multiplication slash division and then addition slash subtraction. So that is our order of operations. Multiplication and division are grouped together. Addition. Subtraction are still group together. If we take a look here, it has performed the following calculation to the right number of sig figs. We have in brackets 1.8 nine times. 10 to the six times 3.5 Then we have 5.21 to the third, divided by 8.8 to 9, minus 6.5 plus 2.920 All right, so we're following our order of operations and in our order of operations, we're gonna do what's in here first because we have brackets and parentheses here. So we're gonna say when we do everything inside of here when we multiply everything. It comes out to But when you're multiplying or dividing numbers, we have to look at the least number of sick fix. So here this number has three sig figs. This number here has four sick fix. So our answer at the end when they multiply, has to have three sig figs. So this initial answer that I got here becomes 5.68 times 10 to the six after I've changed it into scientific notation. Next, we have 5.21 to the third, so that's exponents. So all this means is 5.21 times 5.21 times 5.21 All of them are multiplying each other. All of them have three sig figs. What we would get initially from it is 141. But again, when you're multiplying its least number of sig figs. So our answer would have to have three sig figs. So here, this will come out to be 1 41. Okay, Next we have what's on the bottom here. 8.29 minus 6.5 if you're adding or subtracting its least number of decimal places. So what we would get initially is 2.3 to 9 when we subtract. But this number here has three decimal places. This one here has one decimal place. So our answer at the end must have one decimal place. So that will come out to be 2.3 as our number here next we have plus 2. Okay, Mhm. So we're looking at this portion down here. Now we continue onward now the two numbers on the top on multiplying each other because they're multiplying, it still least sig figs. Here the coefficient has three sig figs and here 1 going the other way because it doesn't have a decimal place. 1 41 has three sig fix. So our answer at the end must have three sig fix when they multiply together comes out as 8.1 times 10 to the eight notice I'm not putting everything all at once. In my calculator you have to do a piece by piece in orderto isolate your final answer. Then on the bottom, these two are adding together. So when they add together. Initially, it comes out as a 5.2 to 0. But when you're adding or subtracting its least number of decimal places, this one here has one. This one here has three. So your answer at the end must have one decimal place, so that would be 5.2. Now, we just have these two numbers that are dividing each other. So again, it's least number of sig figs. This 8.1 has three sig figs in it. This five to has to sig figs in it. So our answer at the end must have to sick fix. So this comes out as 1.5 times 10 to the eight. So this would be our final answer written to the correct number of significant figure based on this mix of operations. So just keep in mind the order of operations to guide you on what to do and remember. Multiplication and division is least sig figs, addition or subtraction is least decimal places