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# Scientific notation word problem: U.S. national debt

Ever wonder what your part of the national debt is? It might surprise you. What isn't surprising is that you can use scientific notation and division to figure out the answer. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• I often wonder about when is the correct time to round a number during a calculation. At you rounded to the fourth decimal place. Should you wait to round until you have moved the decimal for the last time? Making it 3.9786*10 to the 4th?
I have gotten the answer wrong by not rounding during the problem, but it is less accurate too.
Am I correct in rounding after, or should it occur during the problem calculation?
• You should estimate (round) an answer only at the very end, not before that.

Although, for most of the calculations, rounding up to the 6th or 7th place is enough to still get a precise answer at the end. I'd just like to make it clear that this is NOT a fact, this is only my personal opinion based on thousands of exercises I've done.
• In he changes 10^8 into 10^-8. How does this work. Wont that change the outcome? Please explain.
• So, look carefully between and - in first case you have a fraction (10^13)/(10^8), where 10^8 is under the fraction; afterwards, Sal transformed the division into multiplication, where the number under the fraction is with a negative exponent, tha's how 10^13 divided by 10^8 becomes 10^13 multiplied by 10^-8;
• I don't understand, where did you get the number 9 when the number said .3978 (in the calculator)
• When he divided 1.2278 by 3.086, The calculator gave him: .397861 The question said to round to four decimal places. The number in the fourth place is 8, so when you want to round it, look at the number to the right of it ( which is the lesser number) That number is 6. If the number is 4 or below, keep the number the same, if it's 5 or above, round the number up. Since 6 is above 5, you would round the 8 to a 9.
• Jesus Loves You =)
• why did the eight turn into a negative 8 in ?
• Because 1/10⁸ is the same as 10⁻⁸.

When you move a number with an exponent from the numerator to the denominator (or from the denominator to the numerator), you must change the sign of the exponent.
• I don't understand why it's 10^4? He moved it one to the right. Wouldn't it go from 10 ^5 to 10^6? I"m confused, 0.3979, you move it 1 to the right (multiply by 1) to make it 3.979. So wouldn't you add 10^5 + 10^1=10^6. But the exponent went from 10^5 to 10^4. Doesn't that only happen when you divide by 1? The decimal point was moved 1 to the right, not to the left...?
• When you move the decimal point one to the right, you multiply the decimal by 10. So, you have to adjust the exponent to compensate for that. Hence, you divide 10^5 by 10 and get 10^4.

Essentially you multiply the number by 10 and divide it by 10. So you didn't change the value, only the expression.
• What is the u.s census bureau?
• "The United States Census Bureau (or USCB) is a principal agency of the U.S. Federal Statistical System responsible for producing data about the American people and economy." - Wikipedia
• Around Sal said 10^13/10^8 = 10^5 , What if it was 10^-13/10^8 or 10^13/10^-8.. Do I subtract regularly like 13-(-8) or -13-8?
• 10^-13/10^8 = 10^-13 * 10^-8 = 10^-21
10^13/10^-8 = 10^13 * 10^8 = 10^21
• At , does everyone really owe that much or do some people owe more than others?
• Our national debt is not directly allocated to individual people. You will sometimes seem problems like the one in the video that show the average amount every person would owe to pay of the debt. This gives you a sense of how large the debt is.

In reality, our federal income tax is used to pay for federal expenses. Individuals and companies pay income tax. And, the rates are based on income levels. So, the average cost per person does not directly align to how taxes are paid.
• If you were to solve:

4.82/5.16 times 10 to the first/ 10 to the sixth

what would happen to 4.82/5.16?
• Hi, evilcupcake6663

First off, 4.82 divided by 5.16, followed by multiplication by 10^1 divided by 10^6, yields 0.934 multiplied by 10^-5 - but the number 0.934 is NOT greater than or equal to 1 AND less than 10. Thus, we have to multiply 0.934 by 10; to make it so that it results in a number that is greater than or equal to 1 and less than 10 - or, in other words, shift the decimal one place to the right - in order to express it in proper scientific notation, which equals 9.34; but because we are multiplying it by 10, we have to take off a power from our 10^-5 yield from before - in other words, 9.34 multiplied by 10^1, followed by multiplication by 10^-5; but remember, when you multiply powers, you are effectively subtracting them away. So, in our case, 10^1 multiplied by 10^-5, yields 10^-4.

Final answer: 9.34 multiplied by 10^-4.

I hope this helps. Feel free to ask further questions if you seek clarification.

Happy math-ing!