In Exercises 31–50, perform the indicated computations. Write the...

Question

In Exercises 31–50, 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.(4.3X10⁸)(6.2X10⁴)

Accepted Answer

Hello, today we're going to be multiplying the following numbers than expressing the result in scientific notation with two decimal places. So what we are given is six times 10 to the power of five, multiplied by 3.9 times 10 to the power of four. Now, in order to multiply two numbers that are in scientific notation, we're going to have to multiply the real numbers with each other and multiply the exponential numbers with each other. So doing this process is going to give us six times 3.9, which is going to give us the value of 23. And 10 to the power of five times 10 to the power of four can be simplified by using our exponential multiplication. See exponential multiplication allows us to add the exponents together. Since we're multiplying two numbers with the same base of 10. So this can be simplified as 10 to the power of five plus four and 10 to the power of five plus four is equal to 10 to the power of nine. So the product of the two given numbers is equal to 23.4 times 10 to the power of nine. But keep in mind that we want to express the answer with two decimal places In order to do this, we're going to have to take our decimal and move it one unit to the left. But if we move it one unit to the left, we're going to have to add one to the exponent of 10 since we're making 23.4 smaller by a factor of 10. So the product of the two numbers can be rewritten as 2.34 times 10 to the power of 10. And this is going to be the product for the two given numbers. And with that being said, the answer to this problem is going to be c so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 31–50, 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.(4.3X10⁸)(6.2X10⁴)

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