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.3.6X10⁴ / 9X10⁻²

Accepted Answer

Hello, today we're going to be dividing the two given numbers than expressing the results in scientific notation with two decimal places. So what we are given is 3.9 times 10 to the power of five divided by six times 10 to the power of negative three. Now, in order to divide two numbers in scientific notation, we're going to have to divide the real numbers with each other and divide the exponential values with each other. So let's go ahead and simplify this 3.9 divided by six is going to give us the value of 0. And 10 to the 5th divided by 10 to the negative third is going can be reduced by using our exponential division. And we can rewrite the statement as 10 to the power of five minus negative three. Now, since we're subtracting a negative number, we can go ahead and rewrite that as a sum. So 10 to the power of five minus negative three can be rewritten as 10 to the power of five plus three. And that is going to evaluate to give us 10 to the power of eight. So the current division is going to evaluate to give us 0.65 times 10 to the power of eight. But keep in mind, we want to express our answer with two decimal places. So in order to do that, we're going to have to take the decimal place or the decimal in 0.65 and move it one unit to the right. But in order to move it one unit to the right, we're going to subtract one from the exponent of 10 because we're going to make 0.65 larger by a factor of 10. Thus, the answer can be rewritten as 6.50 times 10 to the power of seven, which is going to be the answer to the division for this problem. And with that being said, the answer to this problem is going to be a. 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.

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.3.6X10⁴ / 9X10⁻²

Key Concepts

Scientific Notation

Division of Exponents

Rounding in Scientific Notation

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