> As to precision it's more accurate to say 3 +/- 0.5 times 101 +/- 0.5 = 256.25 to 355.25 or 305.75 +/- 49.5 than to just say 300.
Ah, problem is you've changed the question now. Which is a reasonable thing to do when face with 3 + 101.5 = ?, but not the point the author was making (or, actually, it is the exact point the author is making) :)
Ehh, I was trying to show why "significant digests" are a poor approximation of accuracy.
His explanation in terms of addition is incomplete. Since "3" only has one significant digit (3.03.0 is a more precise number with 2 significant digits) the answer itself can have no more than one significant figure. 3 +/- .5 + 101.5 +/- .05 = 104.5 +/- 0.55 which has 2 significant digits. Now in his example 3 + 4.7 the three does limit the question to 1 significant digit, but your example has more than that even though your also adding 3 to a number (104.5 +/- 0.55)
PS: This is all assuming the accuracy based on the number of digits given you could easily have 3 +/- .0001 and 101.5 +/- 70.
Ah, problem is you've changed the question now. Which is a reasonable thing to do when face with 3 + 101.5 = ?, but not the point the author was making (or, actually, it is the exact point the author is making) :)