Express the product of 4.0 x 10^-2m

Question

Accepted Answer

Hey there folks, welcome back. Alright, so for this answer we want the answer with the correct number of significant figures for the following calculation. So what we have here is numbers in scientific notation and we're multiplying them together. So let's take a look. So we have six point oh times 10 to the fourth. So that's one number. So we're going to put that in parentheses when we do put these numbers into the calculator, then we have 6.783 times 10 to the negative three. That's a second number. And then the third one is right here, 2.98323 times tend to be second power. Right? So here we're just multiplying them. Now, remember when we do multiplication or division? We want our final answer to have the least number of significant figures. Let's go ahead and count the number of significant figures in each of these numbers. So the times 10 to the coefficient is actually not part of the significant figures, so you don't really count those. So for the first one we have 12, right, So all three of these numbers have a decimal place. So we're going to start from the left counting from the left and go to the right. The 1st 10, 0 number will be our first one. So we have six and 0. So that's two significant figures. Alright, so for the second number, we have 1234, that is four significant figures. And then the third one we have 123456, that's six. So obviously to is the least the smallest number. So our final answer will have two significant figures which actually tells us that A and B are out of the answers because they do have more than two significant figures. The first one in fact is going to have an infinite number of significant figures because it doesn't have a decimal place and it ends with zeroes. Alright, so let's go ahead and put these numbers into the calculator again. Make sure that you're putting parentheses around each of these numbers in your calculator. Otherwise you're going to get a number that just doesn't make sense. So when you do that You should get 1.21411 And it's going to be times 10 to the 5th. Right? So but we said we wanted to significant figures. Right? So we want this one and then we want this to that will give us two significant figures. We always take a look at the number that is next to the last significant figure. If it's five or above then we have to round up the last number. If it's below that then we can just ignore it. So because it's one we don't need to round up we're just gonna you know Leave it as as two. So the answer will be 1.2 and then of course the exponent is the same times 10 to the fifth. Okay, so it's not to the ninth but to the fifth. So it looks like option D. Here is our final and correct answer. Right brooks. Thank you so much for watching, and we'll see you in the next video.

Express the product of 4.0 x 10^-2m

Watch next