jmc

We could write out all of the terms until we get to the tenth term, but instead we can find the formula for the $n$th term in the geometric sequence. Since 9 is the first term and we multiply by $\frac{1}{3}$ to find the next term, we determine that the formula for the geometric sequence is $a_n=9\cdot {\left(\frac{1}{3}\right)}^{(n-1)}$. That means $a_{10}=9\cdot {\left(\frac{1}{3}\right)}^9=\frac{3^2}{3^9}=\frac{1}{3^7}=\boxed{\frac{1}{2187}}$.