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Scientific Notation and Unit Conversions

  1. Sep 8, 2012 #1
    "The average wavelength of white light is 5.0 x 10-7m. What would this be in nanometers?

    The textbook answer key stated the answer as 500n but I have no idea how that is the answer.
    I know that the value of nanometers is 10-9 so I figured you add -7 and -9 to get -16...

    Thanks,
     
  2. jcsd
  3. Sep 8, 2012 #2
    [itex] 1 nm = 1 * 10^{-9} m[/itex]

    [itex] \frac{1 nm}{1 * 10^{-9} m} = 1 [/itex]

    [itex] 5.0 * 10^{-7} m = (5.0 * 10^{-7} m) * 1 = (5.0 * 10^{-7} m) * \frac{1 nm}{1 * 10^{-9} m} = ??? [/itex]

    Make sure you keep track of units and it will help you avoid these types of mistakes.
     
  4. Sep 8, 2012 #3

    gneill

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    Staff: Mentor

    Unit conversion is safely accomplished by multiplying your value by terms that are a ratio of 'equal things'. For example, there are 100 cm in one meter, so the ratio "1m/100cm" is effectively equal to 1. If you want to convert 47 cm to meters you would write:

    $$47 cm \times \frac{1 m}{100 cm} = \frac{47}{100}m = 0.47 m$$

    Note how the "cm" units cancel in the expression, leaving just m (meters).
    Can you apply this method to your problem?
     
  5. Sep 8, 2012 #4
    Thank you!
    I understand it now
     
  6. Sep 8, 2012 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This is your basic mistake- this doesn't even make sense! I understand that what you meant was "one nanometer is 10-9 meter" but not writing that leads you astray. From "1 n= 10-9 m" you can get the "unit fraction
    "[tex]\frac{1 n}{10^{-9} m}= 1[/tex].
    So we can write
    [tex] (5.0 \times 10^{-7}m)(1)= \left(5.0 x 10^{-7} m\right)\frac{1 n}{10^{-9} m}[/tex]
    The "m" units cancel but we are dividing fractions so "invert and multiply":
    [tex](5.0 \times 10^{-7})(10^9) n= 5.0 \times 10^2 m[/tex]

     
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