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Exponent Help

  1. Feb 29, 2012 #1

    Drakkith

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    Staff: Mentor

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

    How many inches are in an angstrom, given that 1 angstrom = 10^-8 cm.

    2. Relevant equations
    1 angstrom = 10^-8 cm
    1 inch = 2.54 cm


    3. The attempt at a solution

    Ok, I convert 1 angstrom to 10^-8 cm, then divide by 2.54. This gives me 3.94 x 10^-8, but the book says it's actually 3.94 x 10^-9. What did I do wrong with the exponents? Is 10^-8 the same as 10 x 10^-8?
     
  2. jcsd
  3. Feb 29, 2012 #2
    no it's not, 10 is 101, so 10 x 10-8 is (101)(10-8) which is 101-8 which is 10-7

    btw: I really hate angstroms ;_; they make life a pain in the butt because of things like this
     
  4. Feb 29, 2012 #3

    Drakkith

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    Staff: Mentor

    So is 10^-8 = 1x10^-8?
     
  5. Feb 29, 2012 #4
    yeah, you're multiplying it by 1, A = 1*A
     
  6. Feb 29, 2012 #5

    Drakkith

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    I don't follow you. Isn't 10^-8 equal to 0.0000001 while 1x10^-8 equal to 0.00000001? (6 zeros in the first, 7 in the second)
     
  7. Feb 29, 2012 #6
    I plugged 10^-8 into my calculator and got 0.00000001 which has six zeros

    I did the same with 1x10^8- and got 0.00000001 as well
     
  8. Feb 29, 2012 #7

    Drakkith

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    Staff: Mentor

    Both those have 7 zeros.
     
  9. Feb 29, 2012 #8
    whoops you're right

    but still, they're the same

    1*A = A

    and so if A = 10^-8, then 1*10^-8 = 10^-8



    remember that ab = [itex]\frac{1}{a^{-b}}[/itex]

    so in our case we have 10-8 = [itex]\frac{1}{10^{8}}[/itex]

    so then 1(10-8) = [itex]\frac{1}{10^{8}}[/itex]
     
    Last edited: Feb 29, 2012
  10. Feb 29, 2012 #9

    Drakkith

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    Staff: Mentor

    Ok, from wikipedia: In the base ten (decimal) number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 10^3 = 1000 and 10^−4 = 0.0001.

    So 10^-8 = 0.00000001, aka 1x10^-8.
    Now it makes sense.
     
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