1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar

    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


    User Avatar

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted