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On February 2, 2010 the U.S. Treasury estimated the

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national debt at 1.2278 times 10 to the 13th power.

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And just to get a sense of things, 1 times 10 to the

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sixth is a million, 1 times 10 to the ninth is a billion, 1

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times 10 to the 12th is a trillion.

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So we're talking on the order of magnitude

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of 10 trillion dollars.

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So this is about 12 trillion dollars.

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Then they tell us that the U.S. Census Bureau's estimate

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for the U.S. population was about 3.086 times 10 to the

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eighth power.

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So this is a little over 300 million people.

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So that's an interesting number right there, it's the

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population.

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And then they say, using these estimates calculate the

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per-person share of the national debt.

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So essentially, we want to take the entire debt and

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divide by the number of people.

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That'll give us the per-person share of the national debt.

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Use scientific notation to make your calculations and

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express your answer in both

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scientific and decimal notation.

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Which means just as a regular number.

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Round to four decimal places while making calculations.

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So we want the per-person debt.

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So we want to take the total debt and divide by

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the number of people.

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So the total debt is 1.2278 times 10 to the 13th.

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And we want to divide that by the total number of people,

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which is 3.086 times 10 to the eighth.

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And we could separate this into two division problems. We

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could say that this is equal to the division right here,

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1.2278 divided by 3.086.

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And then times 10 to the 13th divided by 10 to the eighth.

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Now, what's 10 to the 13th divided by 10 to the eighth?

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Let me do it over here.

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The way I think about it, this is the exact same thing as 10

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to the 13th times 10 to the negative eight.

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This is an eight right here.

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If you have a 10 to the eighth in the denominator, that's

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like multiplying by 10 to the negative eight.

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So you have 13, you the same base 10, so 10 to the 13th

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times 10 to the negative eight is going to be 10 to

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the 13 minus 8.

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Which is 10 to the fifth.

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Or another way to think about it: If you have the base in

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the denominator, you subtract the exponents.

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So it's 13 minus 8.

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10 to the fifth.

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So it's this blue expression times 10 to the fifth.

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And let's get a calculator out to calculate this right here.

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And they say round everything to four decimal places, so

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I'll keep that in mind.

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Let me turn my calculator on.

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1.2278 divided by 3.086 is equal to 0.3979.

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Because we want to round right there.

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Let me remember that.

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Or let me just put it on the side so I can

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still look at it.

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So this this little dividing decimals

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problem results in 0.3979.

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And of course, times 10 to the fifth dollars per person.

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Once again, you might be tempted to say, hey this is in

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scientific notation.

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I have some number times a power of ten.

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But notice, this number is not greater than or equal to 1.

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Remember, this number, if you want to be formal about

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scientific notation, has to be greater than or equal to 1, or

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less than 10.

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So what we can do here is we can multiply.

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If we don't want to change the number, we can multiply this

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number by 10 and divide this number by 10.

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Or another way you can think about it is, this whole thing

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can be rewritten as 0.3979 times 10

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times 10 to the fourth.

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What I did was just now was I broke up the 10 of the fifth

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into a 10 and a 10 to the fourth.

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And I did that because I want to multiply this by 10 so I

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can get a 3 out front instead of a 0.3.

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So let's do that.

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So essentially, I took a 10 out of the 10 to the fifth.

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I divided it by 10, I multiplied this other guy by

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10, not changing the whole number.

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So then this right here will become 3.979 and then times 10

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to the fourth.

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So that's how much debt there is per-person

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in scientific notation.

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Now, in the problem they also wanted us to express it in

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decimal notation.

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Which is just kind of standard writing it as a number with

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our standard numeric decimal system.

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So what is 3.979 times 10 to the fourth?

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Let's think about it.

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Well let me just do it this way.

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Let's just move the decimal space.

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If we multiply it by 10, we're going to get 39.79.

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If we multiply it by 10 squared, we're

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going to get 397.9.

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If we multiply it by 10 to the third, we're

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going to get 3,979.

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If we multiply it by 10 to the fourth, we're going to get one

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more zero right there.

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So we're essentially going to move the

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decimal four to the right.

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So I could write it like this.

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This is equal to $39,970.

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So if you think about the national debt per person.

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Every man, woman, and child in the United States essentially

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owes $39,970.

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