Dimensional analysis. Conversion factor confusion

  1. 1. The problem statement, all variables and given/known data
    How many centimeters are there in 3.25 miles?


    2. Relevant equations
    So basically, convert 3.25 mi to cm.


    3. The attempt at a solution

    [​IMG]
    Uploaded with ImageShack.us

    The teacher put the answer for this problem as 5.16 x 10^5 The teacher used:
    (1609 m/1 mile)(100 cm/ 1 m) as her conversion factor. Why / how is mine wrong? I used the metric prefixes system to get my conversion factor numbers.

    ****(This was done with MS Paint so please disregard the 3rd grader hand writing.)
     
  2. jcsd
  3. berkeman

    Staff: Mentor

    You have a misplaced decimal point in your answer, but that could be left over from Paint.

    Still, I don't know why the teacher's answer isn't 5.23*10^5cm...
     
  4. SteamKing

    SteamKing 9,931
    Staff Emeritus
    Science Advisor
    Homework Helper

    Hint: 1 m = 100 cm
     
  5. Borek

    Staff: Mentor

    That's equivalent to 1cm = 0.01m, both give perfectly valid conversion factors.

    5.23x105 cm it is, there is a mistake in the given answer.

    Even google agrees.
     
  6. Okay. Thanks guys. This clears it up.

    Here's an exact copy and paste of what the teacher's response was:

    3.25 miles (1609 m/1 mile)(100 cm/ 1 m) = 5.16 X 10^5 cm

    So my conversion factor wasn't off. I guess it might have been a mistake.
     
  7. SteamKing

    SteamKing 9,931
    Staff Emeritus
    Science Advisor
    Homework Helper

    The larger point is, by using the conversion 1 cm / 0.01 m in the calculation, the poster multiplied 5229.25 m by 1 cm / 0.01 m. The poster then cancelled the 'm' units and neglected to apply the factor '0.01' in the denominator of the conversion factor. If the poster had used the conversion factor 1 m = 100 cm, it should have been readily apparent that the magnitude of the result in cm should be greater than the measurement in m.
     
  8. berkeman

    Staff: Mentor

    Looks like your teacher accidentally did 3.21 miles instead of 3.25 miles.

    Did you move the decimal point in your answer in time to get full credit?
     
  9. Borek

    Staff: Mentor

    It doesn't hold water, seems to me it is as easy to forget to divide by 0.01 as it is to forget to multiply by 100. If you have enough experience in both cases it is obvious there is something wrong with the final result order of magnitude. If you lack the experience - you will not see it no matter how long you look.
     
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