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Math Help - conversions

  1. #1
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    conversions

    convert 47.3 miles per hour to meters per second
    1mile =1,609 m
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  2. #2
    Senior Member eumyang's Avatar
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    Perform a series of multiplications, keeping in mind your units, so that the units "cancel out" and you are left with the unit you are trying to convert to.

    47.3 miles per hour can be written as
    \left( \dfrac{47.3 \:\text{mi}}{1 \:\text{hr}}\right)

    You've given us the conversion factor 1mile =1,609 m. So we'll write that as a ratio and multiply it by the first fraction above:
    \left( \dfrac{47.3 \:\text{mi}}{1 \:\text{hr}}\right)\left( \dfrac{1609  \:\text{m}}{1 \:\text{mi}}\right)
    I put the meters on top and miles on bottom so that the miles units "cancel out."

    Now we have to convert from hours to seconds. There are 3600 seconds in 1 hour, so we have another multiplication:
    \left( \dfrac{47.3 \:\text{mi}}{1 \:\text{hr}}\right)\left(  \dfrac{1609  \:\text{m}}{1 \:\text{mi}}\right)\left(  \dfrac{1  \:\text{hr}}{3600 \:\text{sec}}\right)
    I put the hours on top and seconds on bottom so that the hours units "cancel out"

    When all the units "cancel out" I will be left with meters on top and seconds on the bottom -- meters per second, which is what we want. All is left is to multiply/divide the numbers. I'll let you do that.
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  3. #3
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    thnx eumyang u.ve been like a tutor for me today!
    one more question hod do i write 21.140 in the correct scientific notation?
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  4. #4
    Senior Member eumyang's Avatar
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    2.114 \times 10^1

    Remember that a number in scientific notation must have a single digit between 1 and 9 (inclusive) to the left of the decimal point. So an answer like this:
    0.2114 \times 10^2
    would be wrong, because you can't have just a 0 to the left of the decimal point.
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