0.34 recurring as fraction in simplest form

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.

Learn how to convert the recurring decimal 0.34 (with repeating 34) into a fraction in its simplest form. This detailed step-by-step guide explains how to solve the equation and simplify the result. Ideal for students in Grades 8-10.

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