To evaluate the expression \( \frac{1}{10} \div 0.65 \), we can rewrite the division as a multiplication by the reciprocal:
\[ \frac{1}{10} \div 0.65 = \frac{1}{10} \times \frac{1}{0.65} \]
Next, we need to convert \( 0.65 \) into a fraction. We know that:
\[ 0.65 = \frac{65}{100} \]
We can simplify \( \frac{65}{100} \):
\[ \frac{65 \div 5}{100 \div 5} = \frac{13}{20} \]
Now, the reciprocal of \( 0.65 \) is:
\[ \frac{1}{0.65} = \frac{1}{\frac{13}{20}} = \frac{20}{13} \]
Now substituting back into our expression using the reciprocal:
\[ \frac{1}{10} \div 0.65 = \frac{1}{10} \times \frac{20}{13} = \frac{1 \cdot 20}{10 \cdot 13} = \frac{20}{130} \]
Now, simplify \( \frac{20}{130} \):
\[ \frac{20 \div 10}{130 \div 10} = \frac{2}{13} \]
Thus, the answer in simplest form is:
\[ \boxed{\frac{2}{13}} \]