Problem

Express the results of the following calculations with the correct number of significant figures. (b) ( 5.556 * 2.3)/(4.223 - 0.08)

Relevant Solution
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Hey there. Welcome back. Alright, so here, how many significant figures does each arithmetic calculation have? So here we have three different calculations. We're going to take a look at the first one. Alright, so in the first one, what we're doing is we're adding. Right so whenever we're adding we're going to take a look at decimal places. We want our final answer to have the least number of decimal places as possible. So both of these numbers have one too. They have two decimal places which means our final answer should have two decimal places. Right? So let's go ahead and add this. Just put that into your calculator and see what we get. So we get 1, 0.55. Right? So here we actually have 12. We have two decimal places which is the correct um correct answer. So how many significant figures does this answer have? Well since here we have a decimal place, we're going to start from counting from the left and go to the right. The 1st 10 0 number is one. So let's just go ahead and count. We have 123456. So this one has six significant figures. Okay, so it looks like the only correct answer or the option here that we have for the first one to have six is the so that is most likely going to be our our answer but let's go ahead and actually do all of the work for the second and the third. So for the second and for the second one we're doing multiplication and division for that, we need to count the number of significant figures. Right? So in the first number we have three significant figures because we're starting to count from the left, going to the right, right. So this is three significant figures. The second number we have 12344 and then this one we have 1234 as well. Alright, so we know that our final answer should have three significant figures. And that actually makes sense with the with the answer option here. But let's let's see why it is three significant figures. So we're going to go ahead and do the multiplication first. So 8.00 times 12.67. When you put that into your calculator, you're going to get 101.36. Right? So if we were to get this as a final answer, this is actually the wrong number of significant figures. Because between these two numbers, three was the least number of significant figures. So this would actually we would drop this .36 and it would just be 1, 101. Alright, so just be 101. So that will give us a number of significant figures as three. Then when we divide that By 2.39, 2 again, So we're dividing we're looking at a number of significant figures. This one has three. This one has four. So we want our final answer to have three. Right, So we have we get 442.224. That's what my calculator gave us. But because we only want to three significant figures, here's 12 and three. So that's all we want. So the final answer for that. 2nd 1 would be 42.2. Right? And here we have three significant figures. Whoops! Alright, so for the 3rd 1 we're already kind of know there's going to be too. Probably Right, but let's go ahead and do that. So here we have it's a little bit different. Um All right, so we did the second one and now we're doing this third one. So here we actually have multiplication and addition. So obviously we usually do multiplication first. Right, And then addition. And here they are in parentheses. So parentheses do come first. So we're gonna go ahead and multiply these again. Here, we're gonna take a look at the number of significant figures. 28.12 has 1234. Right? It has four significant figures and 9.0, has two significant figures. So for the multiplication part, which should have two significant figures. So 28.12 times 9.0 What we get here is actually 253.08. Right, as the answer. Now, that's not the correct number of significant figures. Right, We want to because that's the least number of significant figures between those two numbers. So we're actually gonna go ahead and convert this number into scientific notation. So all we want is just two and five, right? Five is next to three. So actually we don't need to round up five, it can stay as to five. So we're gonna Uh do 2.5 Times 10. And then here has to be to the second power because we're moving this decimal place two times to the left, so 12, right, so that is the answer for the multiplication of those two numbers. Now we're going to go ahead and add 12.56. Now, whenever we're adding numbers and we have scientific notation we want them to have the same the same exponents. Right? So 12.56 if we were to write that and scientific notation with uh two as a coefficient, it would actually be .12 times tend to the second power. And of course we would put this in parentheses when we're putting this into the calculator because it's you know, it's a scientific notation number. Right? So now that they are in the same, obviously, I'm sorry, like you put both of those numbers in parentheses, so now that we have the same scientific notation or the same coefficient, We're just going to ignore the coefficient for now and we're just going to add 2.5, And that will give us an answer of two 6- 6. and of course the Times 10 to the second is still there. Now we do want how many significant figures? So we started with two from this one. Right? So this one has two Sig figs And this one has actually 1234. So we want our final answer to have to because that's the least number of significant figures. So we want to and six if you take a look at the number that's next to six, it's too So we do not need to round it up. So it would just be 2.6 Times to the second. Okay, so here again, we have two significant figures. So yes, we were correct. D is our final answer are correct. Final answer. Right, folks, thank you so much for watching. We'll see you in the next video.