I have 6 observational data. $L_1,L_2,L_3,L_4,L_5 $ and $ L$. Each of them have seperate error values $\delta L_i$ and $\delta L$. All of these data are numbers such as $1.38e36, 3.45e33, 9.61e41$, etc., their units are the same.When I make the summation I get $L_1+L_2+L_3+L_4+L_5 \approx L$. But I can't find any equality between $\delta L_1+\delta L_2+\delta L_3+\delta L_4+\delta L_5$ and $\delta L$
I tried standart error method which is where $f=L$, $a_i=L_i$
$\delta f= \sqrt{\sum (\frac{\partial f}{\partial a_i}\delta a_i)^2}$
Also I tried to use $\frac{\delta L_1*L_1+\delta L_2*L_2+\delta L_3*L_3+\delta L_4*L_4+\delta L_5*L_5}{L} \approx \delta L$
and also I tried
$\frac{\sqrt{(\delta L_1*L_1)^2+(\delta L_2*L_2)^2+(\delta L_3*L_3)^2+(\delta L_4*L_4)^2+(\delta L_5*L_5)^2}}{L} \approx \delta L$
or $\sqrt{\frac{(\delta L_1*L_1)^2+(\delta L_2*L_2)^2+(\delta L_3*L_3)^2+(\delta L_4*L_4)^2+(\delta L_5*L_5)^2}{L^2}} \approx \delta L$
Nothing is working well. So I cannot calculate $\delta L$. Any ideas or suggestions?
It sounds like you really only have five observations and add them up to get the value for $L$. If that is correct, $\delta L$ is just the sum of the absolute values of the individual errors. In your example the errors have greatly different magnitudes so the sum will be dominated by the largest one.