To find the sum of \( 6.3 \times 10^3 \) and \( 2.41 \times 10^4 \), we first need to express both numbers with the same exponent.
Since \( 2.41 \times 10^4 \) has a higher exponent, we can convert \( 6.3 \times 10^3 \) to the same exponent:
\[ 6.3 \times 10^3 = 6.3 \times 10^3 \times \frac{10^1}{10^1} = 6.3 \times 10^4 \times 0.1 = 0.63 \times 10^4 \]
Now we can add the two numbers:
\[ 0.63 \times 10^4 + 2.41 \times 10^4 = (0.63 + 2.41) \times 10^4 = 3.04 \times 10^4 \]
So, the sum of \( 6.3 \times 10^3 \) and \( 2.41 \times 10^4 \) expressed in scientific notation is:
\[ \boxed{3.04 \times 10^4} \]