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I Number of significant figures in 5*5.364

  1. Mar 3, 2016 #1
    How many significant figures should be present in the answer of 5*5.364?

    1) Addition rule: The result cannot have more digits to the right of the decimal point than either of the original numbers.

    2) Multiplication rule: The result must be reported with no more significant figures as there are in the measurement with the few significant figures.

    Using rule 1: 5*5.364= 5.364+5.364+5.364+5.364+5.364= 26.82

    Ans: 4 significant figures.

    Using rule 2 : 5*5.364= 26.82 = 30

    Ans : 1 significant figure.

    Which one is correct??
     
  2. jcsd
  3. Mar 3, 2016 #2

    DrClaude

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    Staff: Mentor

    It depends where the 5 comes from. If it is itself a measurement, then rule 2 is correct. If it is a pure number, then rule 1 is correct.

    For example, if you are calculating the circumference of a circle, ##C = 2 \pi r##, ##2 \pi## is exact and the number of significant digits for ##C## is the same as for ##r##.
     
  4. Mar 3, 2016 #3
    One would use rule 1 when the "5" (in your example) is known to imply a counted value (usually a unitless number). In such a case, the counted value is exact, and therefore is considered to represent an infinite number of significant figures.

    Rule 2 would apply if, for example, one were calculating work or torque, where each of the numbers represent a measured value of some sort, each with its own implied precision.

    Unfortunately, rule 2 often applies when the exercise is simply arbitrary practice between application of the rule for addition vs. the rule for multiplication. :-(
     
    Last edited: Mar 3, 2016
  5. Mar 3, 2016 #4
    What would you do if nothing is mentioned? My textbook says nothing about what that "5" represents.
     
  6. Mar 3, 2016 #5

    DrClaude

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    Staff: Mentor

    I would take it to be an exact integer. Otherwise, the notation 5. × 5.364 should have been used.
     
  7. Mar 3, 2016 #6
    Taking 5 as integer does get me to the answer in my textbook. Thank you.
     
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