**Rewrite as a simplified fraction.**

\[\large{3.\overline{2} = {?}}\]


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.

Rewrite as a simplified fraction. 3.\overline{2} = {?}

Learn how to convert the repeating decimal 3.\overline{2} into a simplified fraction. This step-by-step solution explains how to use algebra to rewrite the repeating decimal as the fraction 29/9. Suitable for students in Grades 8-10.

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