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.

480,000,000,000 / 0.00012

Accepted Answer

Welcome back. I am so glad you're here. We are asked to divide the following numbers and to express the result in scientific notation with two decimal places if applicable. So the numbers were given are I'm going to write this in a fraction in the numerator, we have 710 billion. So that's 710 followed by nine Zeros and then that's divided by. So our denominator is zero point. Now this is three zeros to the right of the decimal 00034. And our answer choices are a 2.8 times 10 to the 16th. B 2.8 times 10 to the 15th. C 2.9 times 10 to the 15th and D 2.9 times 10 to the 14th. Alright. In order to divide these, the first step is actually to convert these two terms to scientific notation. We recall from previous lessons that scientific notation has one digit to the left of the decimal. That one digit is going to be between one and nine and then it's followed by any other non zero numbers until we just hit zeros that whole thing is times 10 raised to an exponent. And the two terms we have here are both times 10 raised to the zero power because we recall from previous lessons that anything raised to the zero is just one. So multiplying both of these by 10 to the zero is multiplying them by one. But we want to make sure that there's only one digit to the left of the decimal point. And that means we have to move the decimal. So for the numerator for the 710 billion, the decimal is currently way down here on the right hand side at the end and we need to move it to the left. We're going to move it 123456789, 10, 11 units to the left. So we moved to the left 11. When we move to the left, we are going to raise the exponents that the 10 is being raised to. So it's going to this time have zero plus and we're raising it by however many units we moved the decimal. So because we moved it to the left 11 units, we're adding 11 to that zero in our exponent of our 10. So now we can rewrite this. The seven is the one digit to the left of the decimal. Then at 7.1 is the only non zero number there. So it's 7.1 times 10 raised to the and in the exponents, zero plus 11 is 11. And now let's work on the denominator. So we have 0.34. Well, the three is going to be that non zero number to the left of the decimals. We're going to move this decimal units to the right. When we move to the right, we are lowering our decimal or excuse me, not our decimal, we're lowering our exponent by however many units we moved the decimal. So because we moved to the right four, we're going to subtract four from the exponent zero for our 10 to the zero. So we've got in our denominator 3.4 times 10 raised to the zero minus four is negative four. And now that this is in these are both in scientific notation, we can do the division for the parts that are alike. So 7.1 divided by 3.4, 1st 7.1, divided by 3.4 is 2.08823. And then it keeps on going. And then we look back at our instructions and were told to have it to two decimal places. So that means we're going to round two this eight, that is two decimal two places to the right of our decimal. And the eight looks at the eight to the right of it and it says I gotta round up. So this is going to be 2.09 and then it will be times tend to the something we figure out what that exponent is by doing the division for this 10 raised to the 11th, divided by 10, raised to the negative fourth. And we recall from previous lessons that when we have similar bases, so those are the tens, we are going to subtract their exponents. We're going to take 11 minus negative four, which is the same as 11 plus four, which is 15. So this is 10 raised to the 15. And this is our answer in scientific notation, we look at our answer choices for 2.09 times 10 to the 15th and that matches with answer choice. C. Well done. We'll catch you on the next one.

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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. 480,000,000,000 / 0.00012