Now we're dealing with mixed operations. We have a combination of multiplication, division, subtraction, or addition. We're going to say when dealing with this mixture of multiplication, division, addition, and subtraction, we must follow the order of operations. To help us remember the order of operations, we use PENDES, which stands for parentheses, so what's in parentheses is done first, exponents or powers, then we have multiplication/division, and then addition/subtraction. So that is our order of operations. Multiplication and division are grouped together, addition and subtraction are still grouped together. If we take a look here, it says perform the following calculation to the right number of significant figures.
We have in brackets: 1.89 × 10 6 × 3.005 . Then we have 5.21 3 / ( 8.829 - 6.5 ) + 2.920 . Alright. So we're following our order of operations, and in our order of operations, we're going to do what's in here first because we have brackets and parentheses here. So we're going to say, when we do everything inside of there, when we multiply everything, it comes out to 5679450. But when you're multiplying or dividing numbers, we have to look at the least number of significant figures.
So here, this number has 3 significant figures, this number here has 4 significant figures. So our answer at the end when they multiply has to have 3 significant figures. So this initial answer that I got here becomes 5.68 × 10 6 , after I've changed it into scientific notation.
Next, we have 5.21 3 , so that's exponent. So all this means is 5.21 × 5.21 × 5.21 . All of them are multiplying each other, all of them have 3 significant figures. What we would get initially from it is 141.420761. But again, when you're multiplying, the least number of significant figures, so our answer would have to have 3 significant figures. So here, this will come out to be 141.
Next, we have what's on the bottom here, 8.829 minus 6.5. If you're adding or subtracting it's the least number of decimal places, so what we would get initially is 2.329 when we subtract. But this number here has 3 decimal places, this one here has 1 decimal place. So our answer at the end must have 1 decimal place. So that will come out to be 2.3 as our number here. Next, we have plus 2.920. So we're looking at this portion down here now.
We continue onward. Now the two numbers on the top are multiplying each other. Because they're multiplying, it's still least significant figures. Here, the coefficient has 3 significant figures, and here 141, going the other way because it doesn't have a decimal place, 141 has 3 significant figures. So our answer at the end must have 3 significant figures. When they multiply together it comes out as 8.01 × 10 8 . Notice I'm not putting everything all at once in my calculator. You have to do it piece by piece in order to isolate your final answer.
Then on the bottom, these 2 are adding together, so when they add together initially, it comes up as, 5.220. But when you're adding or subtracting, it's the least number of decimal places. This one here has 1, this one here has 3, 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 the least number of significant figures. This 8.01 has 3 significant figures in it. This 5.2 has 2 significant figures in it. So our answer at the end must have 2 significant figures. So this comes out as 1.5 × 10 8 . So this would be our final answer written to the correct number of significant figures 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 are the least significant figures, addition or subtraction is the least decimal places.