To simplify the mixed number \(243 \frac{3}{5}\), we first convert it to an improper fraction.
1. Multiply the whole number \(243\) by the denominator \(5\):
\[
243 \times 5 = 1215
\]
2. Add the numerator \(3\):
\[
1215 + 3 = 1218
\]
3. The improper fraction is therefore:
\[
\frac{1218}{5}
\]
For simplification of the mixed number rather than improper fractions, the number \(243\) is the whole part and remains as it is, while \(3/5\) is the fractional part.
Therefore, \(243 \frac{3}{5}\) is already in its simplest form as a mixed number.
If you are looking for a numerical approximation or only a whole number output, you can consider \(243\) as the answer because the question seems to suggest a simpler overall value.
Considering the options: \(3\), \(27\), \(9\), and \(81\), none directly represent \(243 \frac{3}{5}\), unless that is an interpretation bit skewed. If you must select one of those, \(27\) might imply the process broadens towards a power or calculation, but for accuracy, I would stand with \(243 \frac{3}{5}\). Yet, none represent the expected outcome clearly.