a survey reported that 63.63 repeating & of moviegoers prefer action films. This percent represents a repeating decimal. write that as a fraction

The percentage given is 63.63 repeating, or \( 63.\overline{63} \%\). To convert this repeating decimal to a fraction, follow these steps:

1. **Let \( x = 63.\overline{63} \)**, where the repeating part is 63.

2. **Multiply both sides by 100** to move the decimal point two places:
   \[
   100x = 6363.\overline{63}
   \]

3. **Subtract the original equation from this new one**:
   \[
   100x - x = 6363.\overline{63} - 63.\overline{63}
   \]
   This simplifies to:
   \[
   99x = 6300
   \]

4. **Solve for \( x \)**:
   \[
   x = \frac{6300}{99}
   \]

5. **Simplify the fraction**:
   The greatest common divisor (GCD) of 6300 and 99 is 9. So, divide both numerator and denominator by 9:
   \[
   x = \frac{6300 \div 9}{99 \div 9} = \frac{700}{11}
   \]

Thus, \( 63.\overline{63} \) as a fraction is \( \frac{700}{11} \).

Would you like more details or explanations on any step?

Here are 5 related questions:
1. How can you convert other repeating decimals into fractions?
2. What is the process for finding the GCD of two numbers?
3. Can you verify the fraction by converting it back into a decimal?
4. How would the steps differ for a decimal with more digits in the repeating part?
5. Why do repeating decimals always convert to fractions?

**Tip:** Always check if a fraction can be simplified by finding the GCD of the numerator and denominator.

A survey reported that 63.63 repeating percent of moviegoers prefer action films. This percent represents a repeating decimal. Write that as a fraction.

Learn how to convert the repeating decimal 63.63% into a fraction using algebraic methods. Follow a step-by-step solution to understand how to express repeating decimals as fractions. Suitable for students in Grades 6-8.

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