## U.S. national debt (scientific notation word problem) | Pre-Algebra | Khan Academy

On February 2, 2010 the U.S.

Treasury estimated the national debt at 1.2278 times

10 to the 13th power. And just to get a sense of

things, 1 times 10 to the sixth is a million, 1 times 10

to the ninth is a billion, 1 times 10 to the 12th

is a trillion. So we’re talking on the

order of magnitude of 10 trillion dollars. So this is about 12

trillion dollars. Then they tell us that the U.S.

Census Bureau’s estimate for the U.S. population was

about 3.086 times 10 to the eighth power. So this is a little over

300 million people. So that’s an interesting number

right there, it’s the population. And then they say, using these

estimates calculate the per-person share of

the national debt. So essentially, we want to

take the entire debt and divide by the number

of people. That’ll give us the per-person

share of the national debt. Use scientific notation to make

your calculations and express your answer in both scientific and decimal notation. Which means just as

a regular number. Round to four decimal places

while making calculations. So we want the per-person

debt. So we want to take the total

debt and divide by the number of people. So the total debt is 1.2278

times 10 to the 13th. And we want to divide that by

the total number of people, which is 3.086 times

10 to the eighth. And we could separate this into

two division problems. We could say that this is equal

to the division right here, 1.2278 divided by 3.086. And then times 10 to the 13th

divided by 10 to the eighth. Now, what’s 10 to the 13th

divided by 10 to the eighth? Let me do it over here. The way I think about it, this

is the exact same thing as 10 to the 13th times 10 to

the negative eight. This is an eight right here. If you have a 10 to the eighth

in the denominator, that’s like multiplying by 10 to

the negative eight. So you have 13, you the same

base 10, so 10 to the 13th times 10 to the negative eight

is going to be 10 to the 13 minus 8. Which is 10 to the fifth. Or another way to think about

it: If you have the base in the denominator, you subtract

the exponents. So it’s 13 minus 8. 10 to the fifth. So it’s this blue expression

times 10 to the fifth. And let’s get a calculator out

to calculate this right here. And they say round everything

to four decimal places, so I’ll keep that in mind. Let me turn my calculator on. 1.2278 divided by 3.086

is equal to 0.3979. Because we want to round

right there. Let me remember that. Or let me just put it

on the side so I can still look at it. So this this little

dividing decimals problem results in 0.3979. And of course, times 10 to the

fifth dollars per person. Once again, you might be tempted

to say, hey this is in scientific notation. I have some number times

a power of ten. But notice, this number is not

greater than or equal to 1. Remember, this number, if you

want to be formal about scientific notation, has to be

greater than or equal to 1, or less than 10. So what we can do here

is we can multiply. If we don’t want to change the

number, we can multiply this number by 10 and divide

this number by 10. Or another way you can think

about it is, this whole thing can be rewritten as

0.3979 times 10 times 10 to the fourth. What I did was just now was I

broke up the 10 of the fifth into a 10 and a 10

to the fourth. And I did that because I want

to multiply this by 10 so I can get a 3 out front

instead of a 0.3. So let’s do that. So essentially, I took a 10 out

of the 10 to the fifth. I divided it by 10, I multiplied

this other guy by 10, not changing the

whole number. So then this right here will

become 3.979 and then times 10 to the fourth. So that’s how much debt

there is per-person in scientific notation. Now, in the problem they also

wanted us to express it in decimal notation. Which is just kind of standard

writing it as a number with our standard numeric

decimal system. So what is 3.979 times

10 to the fourth? Let’s think about it. Well let me just

do it this way. Let’s just move the

decimal space. If we multiply it by 10, we’re

going to get 39.79. If we multiply it by

10 squared, we’re going to get 397.9. If we multiply it by 10

to the third, we’re going to get 3,979. If we multiply it by 10 to the

fourth, we’re going to get one more zero right there. So we’re essentially

going to move the decimal four to the right. So I could write it like this. This is equal to $39,790. So if you think about the

national debt per person. Every man, woman, and child in

the United States essentially owes $39,970.

thank u soooooooooooooooo much

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On June 20, 2010.

$(1.3091 * pow(10, 13)) / (3.086 * pow(10, 8)) = $42.420.

Nice, but the next problem won't be so trivial, when the debt holders asking: "Can we give it back? Now!" 🙂

I Love You Man

Interesting…

can you make a nother elimnation video

it was 3978

(1.2278*10^13)/(3.086*10^8) = (12.278*10^12)/(3.086*10^8) = 3.9786*10^4 = US$39,786. So according to the stats in the question, every person in the states owe US$39,786! .

Hey I just wanted to let you know you misread the calculator you read it as 3979 when if you look at it closer you can see its 3978. Just wanted to make sure you could see it 😉

there are mistakes in the answer the scientific notation should be between 9 and 1 not 39