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Significant Numbers

  1. Mar 20, 2008 #1
    Hi,

    I am using a textbook which asks: How far does a commercial jetliner (1046 kilometers/hour) go in 35 milliseconds?

    The reason this isn't in the homework section is because I answered this correctly, but apparently not using the book's version of how to handle significant numbers. Maybe you can help me.

    here are the calculations I did
    1046 kilometers/hour * (1000 meter/1 km) * (1 hr/3600000 ms) * (35 milliseconds)
    or
    1046 * 1000 / 3600000 * 35 = 10.169444444444444444444444444444 -> rounded to 10 meters since 35 has 2 significant figures and the answer should have no more significant figures in a multiplication/division operation than the number with the least significant figures in it.

    The answer given in the textbook is 10.2 (3 significant figures!). Why is the textbook giving 3 significant figures to the answer when a number in the multiplication/division operation clearly has no more than 3 significant numbers in it, but rather has 2. Everywhere I look, this seems to break the rule. I am told everywhere that the answer must not be more than the number in the operation with the least significant figures.
     
    Last edited: Mar 20, 2008
  2. jcsd
  3. Mar 20, 2008 #2

    Mentz114

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    Gold Member

    The numbers given as data, could in fact be exact, couldn't they? And what happens if I write 35ms = 35000 microseconds ?
    In this case, you have not been told the precsion of the data so it's up to you how you express the answer.
     
  4. Mar 21, 2008 #3
    I agree that the answer in the book broke the rule. It should be "10. meters"

    To leave the final answer on a paper, I would first show too many digits and then show the act of rounding it:

    x = (1046 km/hr)(1000 m/1 km)(1 hr/3600000 ms)(35 ms) = 10.16944444 m = 10. m (rounded for 2 significant digits)
     
  5. Mar 21, 2008 #4

    mgb_phys

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    The other way to look at it. You know the time to +/- 0.5ms or about 3% so you quote your answer to around 3% ie nearest 0.3m

    Significant figures aren't necessarily the best approach, ie '10' is accurate to 10% but '98' is accurate to nearely 1% even though both have 2sig fig.
     
  6. Mar 21, 2008 #5

    Andy Resnick

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    2016 Award

    The book answer is (strictly) incorrect, and your answer is preferred- mikelepore's response is the ideal one.
     
  7. Mar 21, 2008 #6

    russ_watters

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    Staff: Mentor

    [edit] Since it is a hypothetical problem, I don't think it is saying the 35 miliseconds is a measurement. It is asking you how far it would go in exactly 35 ms.

    I'd ask for partial credit (if available) based on that logic.

    Is this a high school physics class? I don't recall if in my elementary physics classes we bothered with sig figs. I'm not sure we did.
     
    Last edited: Mar 21, 2008
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