Significant figures:
What is the last digit?
What is the measured value?
Significant Figures and Calculations: Two basic sets of rules:

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.

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 10^{2}.

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