Originally Posted by **Woody** Shouldn't your sum be :
$\displaystyle 2.00 \pm 0.005 \ ft \ + 2.00 \pm 0.005 \ ft \ = \ 4.00 \pm 0.007 \ ft$
If I remember correctly the error tolerance when adding two quantities is not just the sum of the individual tolerances,
rather it is the root of the sum of the squares of the tolerances. |

Perhaps if the plus-or-minus values means the 1 sigma (or 2 , or 3 sigma) values, then yes, the new sigma would be as you describe. But in engineering the plus-or-minus values are actual limits that are acceptable. If I ask a vendor to give me a piece of metal that is 2 feet plus or minus 0.005 feet, they may provide pieces that range from 1.995 to 2.005 feet. So its quite possible that they send me two pieces that are both 2.005 feet long, so their sum would be 2.01 ft.