What is \( 0.6 \overline{32} \) as a fraction? Move numbers to the blanks to complete the fraction.

To convert the repeating decimal \( 0.6\overline{32} \) to a fraction, follow these steps: 1. **Understand the Decimal:** - \( 0.6\overline{32} \) means \( 0.6323232\ldots \), where "32" repeats indefinitely. 2. **Let \( x = 0.6323232\ldots \)** 3. **Multiply to Eliminate the Repeating Part:** - Since "32" has two digits, multiply \( x \) by 100: \[ 100x = 63.2323232\ldots \] 4. **Set Up the Equation:** \[ 100x - x = 63.2323232\ldots - 0.6323232\ldots \] \[ 99x = 62.6 \] 5. **Solve for \( x \):** \[ x = \frac{62.6}{99} \] 6. **Convert to Fraction with Integers:** - Multiply numerator and denominator by 10 to eliminate the decimal: \[ x = \frac{626}{990} \] 7. **Simplify the Fraction:** - Divide numerator and denominator by 2: \[ x = \frac{313}{495} \] 8. **Final Answer:** \[ 0.6\overline{32} = \frac{313}{495} \] **Therefore, the fraction representation of \( 0.6\overline{32} \) is \( \boxed{\dfrac{313}{495}} \).**