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Scientific Notation
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00:01: A water tank holds 1,430,726 gallons of water. Rewrite the amount of water in the water tank using scientific notation. If you remember, scientific notation is another way to write numbers, and you can either write really large numbers or really small numbers. Typically, with scientific notation, you have one number then you have a decimal place and then you might have two or three more numbers and then you have the thousands that you're gonna multiply this by. In order to write this, I have this number right here, 1,430,726. I'm not really gonna pay attention to the 726. To do the scientific notation, I'm gonna use the first three numbers. I'm gonna have 1.43. Now, how does the rest of the number come into place? Well, this is a million. So a million means that after this first number you have six units here before you get to the decimal. That means I'm gonna multiply the 1.43 times 10 to the sixth. What this is saying is that I would take this decimal right here and I would move it six places to the right, which would give me a million. A little bit more than a million 'cause it's 1.43. And that's how you write scientific notation. Let's try another problem. 01:22: The population of Henry County is 143,256 people. The population of Douglas County is 567,800 people. About how many more people live in Douglas county than in Henry County? Write your answer in scientific notation. Okay, first of all, a clue says about and about tells me that I don't have to have the exact number. In order to do this, I'm gonna have to subtract these two amounts and I'm gonna actually round to make it a little bit easier. In Henry County, we have 143,256 people, and I'm gonna round this down to 143,000. It's just gonna make it a little bit easy to do the arithmetic. In Douglas County, we have 567,800 people, and I'm gonna round this up to 568,000. So now I have my two amounts in the two counties and I wanna know how many more live in Douglas County than in Henry County, so I'm gonna subtract. I have to do 568,000 minus 143,000 and I'm gonna get, three from eight is five, four from six is two, one from five is four. So I get 425,000. But I need to write my answer in scientific notation. That's gonna be 4.25 times 10, and this is hundred thousandths, so there's five places to the right of the first number and so that's gonna be times 10 to the fifth.
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How is 14,398 written in scientific notation?
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Write 987.6 in scientific notation.
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Write 0.00634 in scientific notation.
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Answer 1

Here are the numbers in proper scientific notation (coefficient between 1 and 10):

- 14,398 = 1.4398 × 10^4 (moved the decimal 4 places left)
- 987.6 = 9.876 × 10^2 (moved the decimal 2 places left)
- 0.00634 = 6.34 × 10^−3 (moved the decimal 3 places right)