In Exercises 87–106, perform the indicated computations. Write th...

Question

In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (66,000×0.001)/(0.003×0.002)

Accepted Answer

Hi everyone. Let's look at our next problem, perform the indicated operation and express the answer in scientific notation. And we've got 56,000 times. divided by .07 times .004. So since I'm going to want my answer in scientific notation anyway, I've got some very big and very small numbers. The easiest way to start is converting my problem into scientific notation. Again. The whole purpose of scientific notation is to make big and small numbers simpler to deal with. So to start with on the top, I have 56,000 which I'm going to convert into scientific notation. So 5.6 times 1,234, 10 to the 4th power. And it's going to be multiplied by one Times 10. Let's Count 12345 to the -5. That's all that is going to be over. Got 0.7. So that's going to be seven times 10 to the minus two And then .004 which will be four times 10 To the -3. So now we've got two numbers multiplied divided by two numbers multiplied. So let's work this out remembering that when we multiply we add the exponents and when we divide we subtract the exponents. So first let's simplify the top of our fraction here. 5.6 times 10 to the fourth times one times 10 to the minus five. So let's take our first terms 5.6 times one, it's going to be 5.6. And let's figure out our exponent. So four plus negative five. It's gonna give us negative one the exponent of that 10. So 5.6 times 10 to the negative one will now be on top of our fraction And on the bottom we've got seven times four. So 28 times 10 to v. And we've got negative two plus negative three. So 10 to the negative five. So now we're down to a fraction here. So remembering that when we divide we subtract exponents 5. divided by 28, goes twice into 56 but we've got that decimal point so that will give us 0.2 for the answer to that division problem and then negative one minus negative five is the same as negative one plus five. So that's gonna give us 10 to the fourth. Now again to put it in proper scientific notation instead of 0.2, we want to change that into two and then instead of 20.2 times 10 to the fourth, we'll have two times 10 to the third. When we look at our answer choices, we see that choice A. Is two times 10 to the third so there's our correct answer. See you in the next video

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In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (66,000×0.001)/(0.003×0.002)