Significant figures:

What is the last digit?

What is the measured value?

Significant Figures and Calculations: Two basic sets of rules:

1. Addition/Subtraction rule: Significant figures are determined by looking at the decimal place of the numbers being added or subtracted.

   • The number with the "least decimal places" determines the decimal place of the answer,

   • e.g. if we add 1,216,956 to 214.879, the first number has the fewest decimal places, so the answer is rounded off to the 1's place:

   • 1217170.879 goes to 1217171.

1. Multiplication/Division rule: In this case we count the digits. The number with the fewest significant digits determines the number of significant digits in the answer.

   • Note that in this case we are looking at how the error propagates as a fraction of the total (% error), for example

     • for the problem 2.0 x 201 = 402 should be written as 4.0 x 10².

     • This can be understood by doing the problem with upper and lower ranges of the measured number: 1.95<2.0<2.05

       • 1.95 x 201 = 391.95

       • 2.05 x 201 = 412.05

© R A Paselk

Last modified 23 January 2015