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Thread: Significant Figure

  1. #1
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    Question Significant Figure

    Q) Express 2 344.682 8 correct to 3 significant figures.

    Options are

    (A) 2 344 683
    (B) 2 350
    (C) 2 340
    (D) 235
    (E) 234

    To me the answer should be 234 which is E but the answer given is 2340 i.g C

    Why is it C and why we write 0 after 234.To me it will make 4 significant number.
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  2. #2
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    Quote Originally Posted by haftakhan View Post
    Q) Express 2 344.682 8 correct to 3 significant figures.

    Options are

    (A) 2 344 683
    (B) 2 350
    (C) 2 340
    (D) 235
    (E) 234

    To me the answer should be 234 which is E but the answer given is 2340 i.g C

    Why is it C and why we write 0 after 234.To me it will make 4 significant number.
    Trailing zeros in whole numbers are not significant (why? See my alternative solution for a clue).

    If you rounded to the nearest whole number it'd be 2345, which obviously has four significant figures. So you need to round 2 344.682 8 to the nearest decade.

    By the way, a rounded answer of 234 does not seem very close to 2345 .... (common sense should always be used to check an answer).


    Alternatively: In scientific notation your number can be written 2.3446828 x 10^3. If you only want three significant figures, it becomes 2.34 x 10^3 which can obviously be written as 2340.
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  3. #3
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    The point of "significant figures" is to get a number that is still close to the actual number!

    2344.6828- 2340= 4.628.

    2344.6828- 234= 110.6828- that's not at all close!

    Determining whether or not "trailing zeros" are "significant" is a problem. That's why the use of "significant figures" for measurements is almost always allied with "scientific notation".

    2344.6828, to 3 significant figures in scientific notation would be $\displaystyle 2.34 \times 10^3$. The number 2340.6838 to 4 significant figures, in "normal" notation would also be 2340 where it is not clear that the final "0" is intended to be significant. In scientific notation, that would be $\displaystyle 2.340 \times 10^3$ which makes it very clear that the last 0 is significant, otherwise, it wouldn't be written.

    $\displaystyle 2.34 \times 10^3$ could mean any number from 2335 to 2344. $\displaystyle 2.340 \times 10^3$ could mean any number from 2339.5 to 2340.5.
    Last edited by HallsofIvy; Jan 24th 2011 at 10:09 AM.
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