Solution:
To find the sum of
[tex]2.54\times10^{19}\text{ }and\text{ }3.218\times10^{17}[/tex]we have
[tex]\begin{gathered} 2.54\times10^{19}\text{ + }3.218\times10^{17} \\ =(254\times10^{19}\times10^{-2})+(3.218\times10^{17}) \\ =(254\times10^{17})+(3.218\times10^{17}) \\ factor\text{ out the common term,} \\ 10^{17}\times(254+3.218) \\ =10^{17}\times257.218 \\ =2.57218\times10^2\times10^{17} \\ =2.57218\times10^{(2+17)} \\ =2.57218\times10^{19} \\ \end{gathered}[/tex]Hence, the sum is evaluated to be
[tex]\begin{equation*} 2.57218\times10^{19} \end{equation*}[/tex]