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According to link from foregoing comment $a_i$ measurments are inderect, so errors are $$\Delta a_{i}=\sqrt{\sum_{k}\left(\frac{\partial a_{i}}{\partial w_{k}}\Delta w_{k}\right)^{2}}.$$ After calculations it yields \Delta a_{i}= \frac{1}{\left(\sum_{j}\frac{w_{j}}{A_{j}}\right)^{2}A_{i}}\sqrt{\sum_{k}\left( ...