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Really basic question

  1. Dec 19, 2007 #1
    Does 10 to the power of 3 = 1,000 or 10,000? To calculate is do I multiply 10x10=100 then 100x100=10,100 or do I multiply 10x10=100 then 100x10=1,000?

    I know this is a really stupid question but its been a long time since I did basic maths and I've forgotten how this stuff works.
     
  2. jcsd
  3. Dec 19, 2007 #2

    symbolipoint

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    "Power" means "exponent".

    Ten to the power of three means [tex] \[
    10^3
    \]
    [/tex]
     
  4. Dec 19, 2007 #3
    [tex]a^{n} = \underbrace{a \cdot a \cdot a \cdot a \cdot \: ... \: \cdot a \cdot a}_{\mbox{n times}}[/tex]

    [tex]10^{3} = 10 \cdot 10 \cdot 10[/tex]

    Whether you noticed it or not:
    [tex]10^{1} = 10[/tex]
    [tex]10^{2} = 100[/tex]
    [tex]10^{3} = 1000[/tex]
    [tex]10^{n} = 1\underbrace{0000 \: ... \: 00}_{\mbox{n zeroes}} \quad \mbox{n \geq 0}[/tex]
     
  5. Dec 19, 2007 #4

    CompuChip

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    Also works the other way :smile:
    [tex]10^0 = 1[/tex] (a 1 with no zeroes)
    [tex]10^{-1} = 0,1[/tex]
    [tex]10^{-2} = 0,01[/tex]
    [tex]10^{-n} = \underbrace{0,00\ldots000}_{n \text{ zeroes}}1[/tex]
     
  6. Dec 19, 2007 #5
    It is definitely 1000, how did you get 10000 ?
     
  7. Dec 19, 2007 #6

    JasonRox

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    Maybe he thought, take 10 and add 3 zeroes. That is 10000.
     
  8. Dec 19, 2007 #7

    CompuChip

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    As he said in the first post,
    and the answer is of course, you multiply
    10 x 10 x 10 = (10 x 10) x 10 = 100 x 10 = 1000
    just like
    2^5 = 2 x 2 x 2 x 2 x 2 = (2 x 2) x (2 x 2) x 2 = 4 x 4 x 2 = (4 x 4) x 2 = 16 x 2 = 32
    and not
    2 x 2 = 4
    4 x 4 = 16
    16 x 16 = 256
    256 x 256 = 65 536
    65 536 x 65536 = 4 294 967 296
    or something like that

    You passed them. Time to update your signature (or delete 5 posts :smile:)
     
  9. Dec 19, 2007 #8
    Thanks alot. I couldn't remember if it was 10x10x10 or 10x10x100. I was thinking it might have meant multiplying it by itself the amount of times the exponent indicates. For example 10 to the power of 5 I thought it might have been 10x10x100x1000x10000
     
  10. Dec 19, 2007 #9

    CompuChip

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    Nope, a^n is just notation for multiplying a with itself n times, just like n x a is notation for adding it to itself n times.

    10x10x100x1000x10000 would be (10) x (10) x (10 x 10) x (10 x 10 x 10) x (10 x 10 x 10 x 10) = (counting the 10's in there) 10^11.
     
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