1. The problem asks to express the decimal number $3.81$ as a mixed number. 2. A mixed number consists of a whole number and a proper fraction. 3. First, identify the whole number part: $3$. 4. Next, convert the decimal part $0.81$ to a fraction. 5. Since $0.81 = \frac{81}{100}$, write the mixed number as $3 \frac{81}{100}$. 6. Simplify the fraction $\frac{81}{100}$ if possible. 7. The greatest common divisor (GCD) of $81$ and $100$ is $1$, so the fraction is already in simplest form. 8. Therefore, the mixed number is $3 \frac{81}{100}$. 9. Final answer: $3 \frac{81}{100}$.