To express $3.\overline{2}$ as a simplified fraction, we can follow these steps:

1. Let $x = 3.\overline{2}$, where the repeating part is $2$.

2. Multiply both sides of the equation by 10 to move the decimal point: $10x = 32.\overline{2}$

3. Now subtract the original equation ($x = 3.\overline{2}$) from this new equation: $10x - x = 32.\overline{2} - 3.\overline{2}$ $9x = 29$

4. Solve for $x$ by dividing both sides by 9: $x = \frac{29}{9}$

Thus, $3.\overline{2}$ as a simplified fraction is $\frac{29}{9}$.

Would you like any more details on the steps? Here are 5 more questions for practice:

1. Rewrite $1.\overline{6}$ as a fraction.
2. Express $2.\overline{4}$ as a fraction.
3. Convert $0.\overline{3}$ to a fraction.
4. How do you rewrite $4.\overline{7}$ as a fraction?
5. Simplify $5.\overline{8}$ as a fraction.

Tip: When repeating decimals are converted to fractions, they often simplify to a ratio of two integers by manipulating algebraic expressions.