To add the numbers \(3.82 \times 10^{-4}\) and \(1.95 \times 10^{-3}\), we should first express \(3.82 \times 10^{-4}\) in terms of \(10^{-3}\):
\[ 3.82 \times 10^{-4} = 0.382 \times 10^{-3} \]
Now we can add this to \(1.95 \times 10^{-3}\):
\[ 0.382 \times 10^{-3} + 1.95 \times 10^{-3} = (0.382 + 1.95) \times 10^{-3} \]
Now, perform the addition:
\[ 0.382 + 1.95 = 2.332 \]
Thus, we have:
\[ 3.82 \times 10^{-4} + 1.95 \times 10^{-3} = 2.332 \times 10^{-3} \]
So the final answer is:
\[ \boxed{2.332} \times 10^{-3} \]