To solve the expression \( \frac{3}{10} \div \frac{1}{3} \), we can multiply by the reciprocal of the divisor:
\[ \frac{3}{10} \div \frac{1}{3} = \frac{3}{10} \times \frac{3}{1} = \frac{3 \times 3}{10 \times 1} = \frac{9}{10} \]
Therefore, the answer is \( \frac{9}{10} \), which corresponds to option \( C \).