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!