Expression to evaluate: $2.3\overline{8} \div 0.5\overline{4}$

Convert repeating decimals to fractions: $2.3\overline{8} = 2 + \frac{38-3}{90} = 2 + \frac{35}{90} = 2 + \frac{7}{18} = \frac{43}{18}$ and $0.5\overline{4} = \frac{54-5}{90} = \frac{49}{90}$. Divide the fractions: $\frac{43}{18} \times \frac{90}{49} = \frac{43 \times 5}{49} = \frac{215}{49} = 4\frac{19}{49}$.

Many students mistake $0.5\overline{4}$ for $\frac{54}{99}$ instead of $\frac{54-5}{90}$, or fail to correctly convert the mixed repeating decimal $2.3\overline{8}$.

Always convert repeating decimals to fractions before performing arithmetic, as working directly with the decimals often leads to precision errors in competitive exams.