To calculate 9 divided by 1/3, you divide 9 by the fraction 1/3. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/3 is 3.
So, the calculation is:
\[ 9 \div \frac{1}{3} = 9 \times 3 = 27 \]
Therefore, the answer is 27.