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Having trouble with significant figures

  1. Oct 9, 2014 #1
    The problem statement, all variables and given/known data

    Calculate the average speed and average velocity of a complete round trip in which the outgoing 250 km is covered at 95 km/h, followed by a 1.0 h lunch break, and the return 250 km is covered at 55 km/h


    The attempt at a solution
    I know how to calculate average velocity and average speed. But doing these calculations with respect to significant figures is giving me hard times. Since average velocity is 0, I want to explain what I've done in average speed.

    total length = 500km
    --------------------------------------------
    total time = 250/95 + 1.0 + 250/55

    (250/95 = 2.63157895)
    (250/55 = 4.54545455)

    Now, I believe the result of 250/95 must have two significant digits(because denominator and numerator has 2 significant figures), so it should be 2.6.
    Same for 250/55, we have 4.5.

    500/8.1 = 61.7283951. Wouldn't this be 62 when you try to write with two significant figures?

    But the correct answer is 61 according to the answer key. You can get to it by doing the following: (this is my guess to find 61, not anything from the book)
    total time = 2.63157895 + 1.0 + 4.54545455 = 8.1770335
    average speed = 500/8.1770335 = 61.1468695 = 61

    As you see, I really don't know when to care for significant figures. Maybe I've had a false information about these and need to be informed, so I'd be glad if you could help me.
     
    Last edited: Oct 9, 2014
  2. jcsd
  3. Oct 9, 2014 #2
    Okay, now I got a quote from the book.

    "When you divide 2.0 by 3.0, the proper answer is 0.67, and not some such thing as 0.66666666. Digits should not be quoted in a result, unless they are truly significant figures. However, to obtain the most accurate result, you should normally keep one or more extra significant figures throughout a calculation, and round off only in the final results."

    First it says "round off", then "you should be keeping extra digits, and doing this stuff only on final result".
     
    Last edited: Oct 9, 2014
  4. Oct 9, 2014 #3

    gneill

    User Avatar

    Staff: Mentor

    The book is correct. Significant figures are for reported results. When doing calculations keep as many digits for intermediate results as practical. With a calculator with multiple memories that could mean just using the full accuracy of the calculator. If you are documenting your steps for turning in for marking, write down one or two extra digits on intermediate values.

    Never round intermediate values that you will be using for further calculations; Rounding error will eventually creep into your significant digits.
     
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