To add the numbers \(2.54 \times 10^{19}\) and \(3.218 \times 10^{17}\), it's helpful to express them with the same exponent.
First, adjust \(3.218 \times 10^{17}\) to have the same exponent as \(2.54 \times 10^{19}\):
\[ 3.218 \times 10^{17} = 0.03218 \times 10^{19} \]
Now we can sum the two numbers:
\[ 2.54 \times 10^{19} + 0.03218 \times 10^{19} = (2.54 + 0.03218) \times 10^{19} \]
Calculating the sum:
\[ 2.54 + 0.03218 = 2.57218 \]
So, we have:
\[ 2.57218 \times 10^{19} \]
Thus, the sum of \(2.54 \times 10^{19}\) and \(3.218 \times 10^{17}\) is:
\[ \boxed{2.57218 \times 10^{19}} \]
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