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What is the correct way to conver 14,28 m/s to mph and why does the decimal relocate?

  1. Aug 8, 2012 #1

    Sqw

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    This is not a homework question, but it is from a book....

    The book asks:
    In a nuclear chemistry experiment, an alpha particle is found to have a velocity of 14,285 m/s. Convert this measurement into miles/hour.

    I want to verify the correct way to do this, and I also have a question about the decimal point relocating.

    What I did (first):

    14,285 meters per second * 3600 seconds in an hour = 51426000

    51426000 / 1609.344 meters per mile = 31961.467 mph

    The book says the right answer is: 8.2796 x 10^10

    However, when I google " 14,285 meters per second to miles per hour," Google's converter agrees with me...

    But if I do:

    14,285 meters * 1 mile * 60 sec * 60 min / 0.000621371 * 1 sec * 1 min

    I get 82762150148.62296438 Which is almost the same as the book. Except the book has the decimal between the 8 and the 2 and gets 8.2796 instead of 8.2762 which I presume is because they're omitting insignificant numbers during calculation, but I still don't understand how the decimal got moved between the 8 and the 2 while mine is in middle....

    My questions are:

    Which way is correct to convert this?

    And also, more importantly, why does the book move the decimal between the 8 and the 2?
     
  2. jcsd
  3. Aug 8, 2012 #2

    Simon Bridge

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    Re: What is the correct way to conver 14,28 m/s to mph and why does the decimal reloc

    miles per hour??

    That seems awfully fast doesn't it? Reality check - what is the speed of light in mph?

    Note: the book moves the dp because it is using standard scientific notation.
    So 2224 (standard form) = 2.224x103 (scientific notation)
     
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