To find the sum of \( 6.3 \times 10^3 \) and \( 2.41 \times 10^4 \), we first need to express both numbers in terms of the same power of ten.
The number \( 2.41 \times 10^4 \) can be rewritten in terms of \( 10^3 \): \[ 2.41 \times 10^4 = 2.41 \times 10^{4-1} \times 10^1 = 24.1 \times 10^3 \]
Now we can add \( 6.3 \times 10^3 \) and \( 24.1 \times 10^3 \): \[ 6.3 \times 10^3 + 24.1 \times 10^3 = (6.3 + 24.1) \times 10^3 = 30.4 \times 10^3 \]
Next, we express \( 30.4 \times 10^3 \) in proper scientific notation. In scientific notation, we want the coefficient to be between 1 and 10. So, we can write: \[ 30.4 \times 10^3 = 3.04 \times 10^4 \]
Thus, the sum of \( 6.3 \times 10^3 \) and \( 2.41 \times 10^4 \) in scientific notation is: \[ \boxed{3.04 \times 10^4} \]