What are the rules for adding numbers with uncertainties?

[Wombat_of_Doom]

A measured value of 35m is being multiplied by the countable number 3 (say you went 3 times around a track that was 35m long). What's the correct number of sigfigs in the answer?

Method 1:

35 m x 3 = 105m = 110m
By significant digits rules of multiplication, this would be 110m. (The 35m has 2 sigfigs and 3 has infinite because it is a countable number)

Method 2:

35m + 35m + 35m = 105m
By significant digits rules of addition, this would be 105m (All numbers are significant to unit place)

Am I missing something? I can't imagine the precision of your answer being increased by your choice of adding the number 3 times instead of multiplying by 3.

 

[Anon0123]

The increase in precision is a result of going around the track once and obtaining a value of 35m and then multiplying by 3 to approximate the distance traveled going around 3 times vs. going around the track 3 consecutive times and confirming the same measured value of 35m and then summing those values.

 

[haruspex]

To put Anon0123's answer in a different way, when you add numbers with uncertainties you have to consider whether they are independent. If they are, you can suppose that you will not be so unlucky that all the errors will reinforce. I'm not sure what rule for addition you have, but I believe it will only apply to independent random variables.