So, let's say that I measured the lengths of two objects which measured 20 mm and 30 mm. I used the same ruler for both measurements and it has an absolute error of ±1 mm.
If I wanted to calculate the percentage error of the sum of both lengths, correct me if I'm wrong but, it would be this:
$$\text{R%} = \frac{1+1}{20+30}*100$$ $$\text{R%} = 4\text{%}$$
My question is, what if the measurements of those two objects were obtained in a method that involved products or quotients and thus, only an absolute error is provided? i.e. how would I calculate the percentage error of the sum of the lengths if I only know their respective individual percentage errors? e.g. 20 ± 10% and 30 ± 8%
Could I work backwards in the equation like this to obtain a legitimate absolute error: $$10\text{%} = \frac{∆d}{20}*100$$ ...even though in this example, the 20 mm measurement was hypothetically derived through several product and quotient equations?