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Thread: Significant digits.

  1. #1 Significant digits. 
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    Here the question:

    In 1 km races, runner 1 on track 1 (with time 2 min, 27.95
    s) appears to be faster than runner 2 on track 2 (2 min, 28.15 s).
    However, length L2 of track 2 might be slightly greater than length
    L1 of track 1. How large can L2 - L1 be for us still to conclude that
    runner 1 is faster?


    Here's the answer:

    1.4 m

    Blah....



    Why does the text say 1.4 when there is two significant digits? Why is 1.35 m a wrong answer?

    BTW whoever thinks this question is stupid, by all means...
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  2. #2  
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    1.4 is two digits, 1.35 is three digits. Typically two digits should satisfy you unless you need more.
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  3. #3  
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    Maybe I was meaning the the number of decimal places.
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  4. #4  
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    Traditionally 1, 2, 3 and 4 are rounded down while 5, 6, 7, 8, 9 are rounded up.
    This is often overruled in certain contractual and commercial-military-governmental standard situations where 5 can be rounded up or down depending on the rest of the number. This is to prevent unfair skewing of dollars, weights and measures in one direction to the advantage of one party and the disadvantage of the other party.
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  5. #5  
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    But I did round down 1001.351808043258 to 1001.35 to get the 1.35 for two decimal places. It isn't 1.4 so am I still wrong when a text book says 1.4?
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  6. #6  
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    Quote Originally Posted by Beer w/Straw View Post
    Maybe I was meaning the the number of decimal places.
    1.4 has two decimal places
    1.35 has three decimal places.

    the "1" counts as a decimal place also.

    If you want an answer that is accurate to two decimal places 1.4 is the answer, if you want it accurate to three decimal places 1.35 is the answer.
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  8. #8  
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    You need a sense of humour.
    You are oviously tripping on the flowers on the carpet pattern. This means you are attaching importance to something of no importance at all.
    Now if you start saying that it is important; be prepared to tell me how much life, love or money is involved.
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  9. #9  
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    Maybe this is just an isolated example of a myriad. A myriad of things to fail at. Those numbers 28.15 and 27.95, each have precision to two decimal places. Not one.

    Sense of humor? If I lived in the U.S. I would have killed myself by now. Bought a gun, got drunk, and shot myself in the head.
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  10. #10  
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    Do the problem as if track 1 is shorter than a kilometer and see if that makes a difference.
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  11. #11  
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    The more the decimal places, the more the accuracy. Rounding off reduces precision.
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  12. #12  
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    Quote Originally Posted by PhysBang View Post
    Do the problem as if track 1 is shorter than a kilometer and see if that makes a difference.
    The math would only have a chance in changing if I start rounding immediately.
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  13. #13  
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    Oh I see the thing here. Based on the fact that the significant other (er, I mean digits) in the question were 2 (digits to the right of the decmal point) the answer maybe should be 2 digits as well. Beers answer is the right approach (taking the ratio of the seconds taken by each runner and applying it to the lengths). The question is not all that well written to get a super precise answer though as we know at least one of the lengths is not precisely 1000 meters, but we don't know if either is.
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  14. #14  
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    ... I guess I'll fax Cleveland State University.

    The same question is verbatim in more than one edition.
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