To convert $0.34\overline{34}$ (0.34 recurring) into a fraction:

Let: $x = 0.34\overline{34}$

1. Multiply both sides of the equation by 100 to move the decimal point two places: $100x = 34.34\overline{34}$

2. Subtract the original equation $x = 0.34\overline{34}$ from this: $100x - x = 34.34\overline{34} - 0.34\overline{34}$ $99x = 34$

3. Solve for $x$: $x = \frac{34}{99}$

Thus, $0.34\overline{34} = \frac{34}{99}$, which is already in its simplest form.

Would you like any further details or have any questions? Here are 5 related questions you could explore:

1. How do you convert other recurring decimals to fractions?
2. Can any recurring decimal be represented as a fraction?
3. What is the process for converting non-recurring decimals to fractions?
4. How do you simplify fractions after converting from decimals?
5. How does the length of the repeating block affect the process?

Tip: To simplify any fraction, always check for the greatest common divisor (GCD) of the numerator and denominator.