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Let's solve this repeating decimal problem together.

The repeating decimal is \( 0.\overline{01} \), which means \( 0.01010101\ldots \).

### Steps to convert a repeating decimal to a fraction:

1. **Let \( x = 0.\overline{01} \)**.
   
2. **Multiply both sides by 100** to shift the decimal two places to the right:
   \[
   100x = 1.\overline{01}
   \]
   
3. **Subtract the original equation \( x = 0.\overline{01} \) from the new equation**:
   \[
   100x - x = 1.\overline{01} - 0.\overline{01}
   \]
   This simplifies to:
   \[
   99x = 1
   \]
   
4. **Solve for \( x \)**:
   \[
   x = \frac{1}{99}
   \]

Thus, \( 0.\overline{01} \) is equal to \( \frac{1}{99} \).

Do you want more details on any step or have any questions?

### Related Questions:
1. How do you convert \( 0.\overline{001} \) to a fraction?
2. What is the fractional form of \( 0.\overline{123} \)?
3. Can all repeating decimals be converted to fractions?
4. How do you convert a non-repeating decimal to a fraction?
5. What is the difference between repeating and non-repeating decimals?

### Tip:
For repeating decimals, multiplying by powers of 10 helps eliminate the repeating part!

Convert the following repeating decimal to a fraction in simplest form: 0.01̅

Learn how to convert the repeating decimal 0.01̅ into a fraction using algebraic techniques. This problem focuses on key concepts such as converting decimals to fractions and solving simple linear equations. Suitable for students in Grades 6-9.

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