To add \(6.81 \times 10^5\) and \(4.93 \times 10^3\), we first need to express both numbers in terms of the same power of 10. Since \(10^5\) is larger than \(10^3\), we can convert \(6.81 \times 10^5\) to the \(10^3\) format.
\[ 6.81 \times 10^5 = 6.81 \times 10^{5-3} \times 10^3 = 6.81 \times 10^2 \times 10^3 = 681 \times 10^3 \]
Now we can add \(681 \times 10^3\) and \(4.93 \times 10^3\):
\[ 681 \times 10^3 + 4.93 \times 10^3 = (681 + 4.93) \times 10^3 = 685.93 \times 10^3 \]
Thus, the final result is:
\[ \boxed{685.93 \times 10^3} \]