To add the numbers \(6.3 \times 10^3\) and \(2.41 \times 10^4\), we first need to express both numbers in the same power of ten. We can convert \(2.41 \times 10^4\) to \(10^3\):
\[ 2.41 \times 10^4 = 24.1 \times 10^3 \]
Now we can add \(6.3 \times 10^3\) and \(24.1 \times 10^3\):
\[ 6.3 \times 10^3 + 24.1 \times 10^3 = (6.3 + 24.1) \times 10^3 = 30.4 \times 10^3 \]
Finally, we can express this in standard scientific notation:
\[ 30.4 \times 10^3 = 3.04 \times 10^4 \]
Thus, the final result is:
\[ \boxed{3.04 \times 10^4} \]