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Length error which is 2+-1

  1. Nov 3, 2005 #1
    Right having a few labs at the moment and just wanted to get a clarificating conserning errors.

    if i have a length error which is 2+-1... if i add two length or subtract two length, what do i do with the error?
    the same if i multiply them och divide them...

    and then finally if i sqaure,kube or take the sqrt of them..???

    it's not that important could probably ask a tutor but have not lectures today so don't have to get the bus to the uni then =).
     
  2. jcsd
  3. Nov 3, 2005 #2
    for addition and subtraction add the absolute errors.
    For division and multiplication add the percentage errors.
    for cubes and squares etc. multiply the percentage error by the power.
     
  4. Nov 3, 2005 #3

    HallsofIvy

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    Hypercase gave very good "rules of thumb". They are not exactly right but very, very accurate for small errors (surely you can do better than "2+-1"!) and far easier than being precise.

    If you really want to be precise (of course, your "errors" won't be very precise anyway!) you could do this:
    Suppose x is measured at 2+- 0.01, y is measured at 3+- 0.02.
    That means that the true value of x is somewhere between 2-0.01= 1.99 and 2+0.01= 2.01. The true value of y is somewhere between 3- 0.02= 2.98 and 3+0.02= 3.02. The largest possible value for x+ y is 2.01+ 3.02= 5.03.
    The smallest possible value of x+y is 1.99+ 2.98= 4.97. x+y is somewhere between 4.97 and 5.03: 5+- 0.03. Exactly what Hypercase said: the errors added.
    Notice, by the way, that if you subtract the errors do not subtract! They still add. The largest x- y could possibly be is 2.01- 2.98= -0.97, the smallest is 1.99- 3.02= -1.03: x-y is -1+- 0.03- the error is still the sum of the errors.

    Now what about xy? The largest xy could be is 2.01*3.02= 6.0702= 6+ 0.0702. The smallest is 1.99*2.98= 5.9302= 6-0.0698. A bit more complicated! To use Hypercases's suggestion, find the percentage error (also called "relative error") in x: 0.01/2 and in y: 0.02/3.
    Adding those, the percntage error in xy is 0.03/6+ 0.04/6= 0.07/6 and the absolute error is 6(0.07/6)= 0.07: xy is 6+- 0.07 which, while not exact, is pretty darn accurate.
    As Hypercase said, since powers are "repeated multiplication" you do a "repeated addition", i.e. multiplication, of the percentage error.
     
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