To find the sum of \(6.3 \times 10^3\) and \(2.41 \times 10^4\), we first need both numbers to have the same exponent.
We can convert \(6.3 \times 10^3\) into scientific notation with the same exponent as \(2.41 \times 10^4\):
\[ 6.3 \times 10^3 = 0.63 \times 10^4 \]
Now we can add \(0.63 \times 10^4\) to \(2.41 \times 10^4\):
\[ 0.63 \times 10^4 + 2.41 \times 10^4 = (0.63 + 2.41) \times 10^4 = 3.04 \times 10^4 \]
Therefore, the sum of \(6.3 \times 10^3\) and \(2.41 \times 10^4\) expressed in scientific notation is:
\[ \boxed{3.04 \times 10^4} \]