How do we add,subtract,multiply or divide the uncertainities of two values? For example
28.0 +- 0.5 and 0.899 +- 0.003
Actually i have to solve this question
[log{sq.rt. of (0.104 +- 0.006)}/ (.0511 +- 0.0009)]?
Hope u get the question in what manner its written.
When adding or subtracting terms with random error estimates, take the square root of the sum of the squares (RSS) as the probably error of the result.
When multiplying or dividing terms with error estimates, take the square root of the sum of the squares (RSS) of the RELATIVE errors as the relative error of the result.
In your example, the natural log of sqrt (0.104 +- 0.006) is -1.13 (+-3%). The relative error of the denominator is .0009/.0511 = +-0.18%
The relative error of the result is about +- 3%
That would make it -22.1 +- 0.7