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. (4.3×10^8)(6.2×10^4)

Accepted Answer

Hi everyone. Let's look at our next problem. It says perform the indicated operation and express the answer in scientific notation And we have a multiplication problem. Two numbers already in scientific notation. I'm just going to rewrite them since it's split out over two lines to make it a little easier to follow. So we have 5.6 times 10 to the fifth power. And we multiply that by 2.1 Times 10 to the 9th power. And we want to remember that we're more multiplying exponents. We add the exponents. So let's multiply the first terms here. So 5.6 times 2.1. When we do that multiplication we get our answer here and we recall we've got two decimal places. So our answer here is 11.76 but we need to remember so and then that will be our first term here And that will be times 10 to the we've got 10 to the five Plus nine Since we're multiplying So that's gonna equal 11.76 times 10 to the 14th power. But when we write in scientific notation we always want our first term here to be at least one but less than 10 only have something in the ones place. So we just need to rewrite this term. So we're going to shift our decimal .1 place to the left so that we rewrite this as 1.176. But since we essentially divided this term by 10 we've got to make our exponent bigger by a factor of 10. So instead of 10 the 14th. This will be 10 to the 15th. We shifted our desk in place one to the left, so we need to add one to our exponent to the 10. So our answer here is 1.17, 6 times 10 to the 15. And we do indeed have that as choice be and we can double check that. That makes sense because we multiplied two large numbers. We'd expect the result to be even larger. So once again, choice B 1.176 times 10 to the 15th power. Thanks for watching. See you next time.

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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. (4.3×10^8)(6.2×10^4)