Can anybody confirm that my reasoning for the incorporation of the number of decimals is correct here?
I want to calculate the area A of a rectangle with length = 13.727 m and width = 43.313 m. Suppose the error (standard deviation) S on my measurements for the area is 0.34335235 m^2.
Would it then be correct to state that A = 13.727 m * 43.313 m = 594.56 m^2 (only 2 decimals because 5 significant digits in the original data).
However, the standard deviation is apparently always reported with only 1 significant digit so S = 0.3 m^2.
Because the measurement cannot be more precise than its standard deviation, this limits the report of the value to: A = +/- S = 594.6 +/- 0.3 m^2
Thanks