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Significant Digits

  1. Sep 6, 2007 #1
    I just started physics and have a few questions on significant digits.

    I have to put this number into scientific notation

    2 999 900

    My answer is 2.3 * 10 (to the power of 6)
    Is that right?

    My other question is 8.83/0.002 = "4415"
    To write it with sig digits I can only use one because of "0.002"

    So would my answer be 4000?

    And my last question is 8.56 * 2.3= "19.688"
    With sig. digits = 20

    Are these correct?
     
  2. jcsd
  3. Sep 6, 2007 #2
    In the first case, your answer is not quite correct with 2 significant digits. The number you had though, has at least 5 significant digits. The zeros are generally not counted unless there is a trailing decimal placed. Note that 2.9999 doesn't round off to 2.3

    Also, on your last problem, it would be better to put a decimal in to show that the 0 is significant.

    The last significant digit shows where any uncertainty lies - i.e. 245.8 might actually be 245.9 or maybe 245.7. If you measured a quantity, and were fairly certain to within 100 feet and had a measurement of 3,000,000 feet, how could you show where the uncertainty lies? That's another good purpose of scientific notation. You could write the number as 3.0000 x 10^8 feet.

    Easiest rules on sci notation:
    Any digits that aren't a zero always count.
    zeros in front don't count.
    zeros between other non-zero digits always count.
    zeros at the end only count if there's a decimal.
     
  4. Sep 6, 2007 #3
    You need to state to how many significant digits you are using. Say, "to 2 significant digits".

    If it were the case that you need two significant digits, then 2 999 900 in scientific notation would become 3.0*10^6 (the ^ means 'to the power')

    I don't understand what you are trying to say.

    Again you have to state to how many significant figures you are working with.
     
  5. Sep 6, 2007 #4
    It's just multiplying and dividing (in physics) with significant digits.

    In the second one

    8.83/0.002 = "4415"

    4415 isn't the answer because it has to have only 1 significant digit because 0.002 has only one significant digit. So I put 4000 as my answer because it only has one significant digit.
     
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