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Math Help - 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 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 2.340 \times 10^3 which makes it very clear that the last 0 is significant, otherwise, it wouldn't be written.

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