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Simplying a problem with decimals and exponents

  1. Jan 19, 2015 #1

    Anna Blanksch

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    1. The problem statement, all variables and given/known data

    (2.5 x 10^24)(4.5 x 10^-9) / (3 x 10^4)

    2. Relevant equations


    3. The attempt at a solution

    I know that when multiplying base ten numbers with exponents you add the exponents (ie: 10^2 x 10^3 = 10^5) ad that when dividing, the exponents are subtracted. I'm not sure what my first step would be towards simplifying this equation.
     
  2. jcsd
  3. Jan 19, 2015 #2

    Dick

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    Split it into ((2.5 x 4.5)/3) x ((10^24 x 10^(-9))/10^4). Use your exponent rules on the second factor and a calculator on the first factor.
     
  4. Jan 19, 2015 #3

    Anna Blanksch

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    Great! Thanks for your help. Is there a rule/title for the process of converting from the original problem to the way that you split it (separating the base ten numbers)? Also, am I calling those the right thing? Base ten numbers? Should they be called, "base ten exponents"? The answer I got is 3.75 x 10^11. Close? Right on? Thanks again so much for your quick reply!
     
  5. Jan 19, 2015 #4

    Dick

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    Right on. I call them "powers of ten", and I don't think it has a name. It's just separating the powers of ten from the other numbers.
     
  6. Jan 19, 2015 #5

    SteamKing

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    What you are seeing is an application of the associative property in multiplication:

    http://en.wikipedia.org/wiki/Associative_property

    You can use this property to group strings of numbers being multiplied together into more convenient arrangements.

    For example:

    (2 * 3) * 4 = 2 * (3 * 4) or
    (2 * 103) * (4 * 102) = (2 * 4) * (103 * 102) = 8 * 105
     
  7. Jan 19, 2015 #6

    BvU

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    Poor Anna, in the middle of nitpicking nerds !

    I can't resist to point at the sentence "Associativity is not to be confused with commutativity, which addresses whether a × b = b × a." in his majesty's link. However, you need it to get from where you were to where you want to be.

    If you go on in maths or physics this kind of attention to detail is essential; for the rest of the world it's just a good idea :)
     
  8. Jan 19, 2015 #7

    SteamKing

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    It's learning the simple things which seems to be overlooked nowadays. Everybody wants to split the atom; nobody wants to learn to use a hammer.
     
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