The Wikipedia page for Significance arithmetic uses this example in the rules for addition:
9.9
9.9
9.9
9.9
3.3
+ 1.1
----
40.0
Each addend has two significant figures, and the result has three, because the 4 is carried over from the addition in the ones column. What I don't understand is why the answer isn't 44.0. How is the 4 in the ones place rounded out of the result? If the 4 is carried over from the addition in the ones column then why isn't the 4 carried over from the addition in the tenths column?
Following the rules, as I understand them, and adding step-by-step, we have:
9.9 + 9.9 = 19.8
Since the addends have two significant figures the result needs to be rounded to two significant figures, and we retain the tenths column because it is also significant, so 19.8 ≈ 20.0.
Next, we have:
20.0 + 9.9 = 29.9
9.9 has the fewest significant figures, so we again round, and 29.9 ≈ 30.0.
Continuing in this manner, we get:
30.0 + 9.9 = 39.9 ≈ 40.0
40.0 + 3.3 = 43.3 ≈ 43.0
43.0 + 1.1 = 44.1 ≈ 44.0
Am I doing something wrong, or is the wiki answer wrong?
This wikipedia page makes little to no sense. When you're doing addition with significant figures you want to carry out all the operations and then simply at the end.
For instant 9.9 + 9.9 + 9.9 + 9.9 + 3.3 + 1.1 = 44.0 We should have 2 sig figs, so the answer really should be 44.