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The repeating decimal you are working with is \(0.\overline{29}\), which means the digits "29" repeat infinitely. To convert this into a fraction, follow these steps:

1. Let \( x = 0.\overline{29} \).
2. Multiply both sides by 100 to shift the decimal point two places to the right:  
   \( 100x = 29.\overline{29} \).
3. Subtract the original equation \( x = 0.\overline{29} \) from this new equation:  
   \[
   100x - x = 29.\overline{29} - 0.\overline{29}
   \]
   This simplifies to:  
   \[
   99x = 29
   \]
4. Solve for \( x \):  
   \[
   x = \frac{29}{99}
   \]

Thus, \( 0.\overline{29} = \frac{29}{99} \).

This fraction is already in its simplest form since 29 and 99 have no common factors other than 1.

Would you like more details on this solution or have any other questions?

Here are five related questions you might find helpful:
1. How do you convert repeating decimals with more than two repeating digits to fractions?
2. What is the general formula for converting repeating decimals to fractions?
3. How do you simplify a fraction once you convert a repeating decimal?
4. Can every repeating decimal be expressed as a fraction?
5. What is the process to convert a mixed repeating decimal (e.g., 0.234\(\overline{5}\)) to a fraction?

**Tip**: Always check if the resulting fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

Convert the following repeating decimal to a fraction in simplest form: 0.29 where 29 repeats indefinitely.

Learn how to convert the repeating decimal 0.29, where 29 repeats indefinitely, to a fraction. This guide covers algebraic methods, specific formulas used, and detailed steps to simplify the process, ideal for middle to high school students.

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