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Math Help - Significant digit? how to work this out?

  1. #1
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    Significant digit? how to work this out?

    Hi.

    I would like to ask those that have done a bit on computational Maths.
    I thought I understood it but my lecture notes gives another example and i don't get it:

    It reads:
    actual value = 23.496 and estimate = 23.494
    The the error is |actual - estimate|= 0.002.
    The actual value has four signifi cant digits with respect to actual value , since the error is less
    than 5 in the fifth place to the right of the first nonzero digit in actual . Note that if estimate
    is rounded to four places, an additional error is introduced and estimate will no longer have four signi ficant digits.

    What does even this mean? I don't get it. Please someone explain for me.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Significant digit? how to work this out?

    Quote Originally Posted by willy0625 View Post
    Hi.

    I would like to ask those that have done a bit on computational Maths.
    I thought I understood it but my lecture notes gives another example and i don't get it:

    It reads:
    actual value = 23.496 and estimate = 23.494
    The the error is |actual - estimate|= 0.002.
    The actual value has four significant digits with respect to actual value , since the error is less
    than 5 in the fifth place to the right of the first nonzero digit in actual . Note that if estimate
    is rounded to four places, an additional error is introduced and estimate will no longer have four significant digits.

    What does even this mean? I don't get it. Please someone explain for me.
    I don't get it either but there are a large numbers of ways to do this. Check with your instructor. I would say your answer should be: 23.494 \pm 0.002.

    -Dan
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  3. #3
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    Re: Significant digit? how to work this out?

    This is his definition:

    In place of relative error, we often use the concept of signifi cant digits. we say estimate has m
    signifi cant (decimal) digits with respect to actual if the error (actual - estimate) has magnitude less
    than or equal to 5 in the (m+1)st digit of actual , counting to the right from the first nonzero
    digit in actual .


    Does it help?
    Thanks from topsquark
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