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The problem shows \(0.\overline{715}\), which represents a repeating decimal where the digits "715" repeat indefinitely.

To convert this repeating decimal into a fraction, we can follow these steps:

### Step 1: Define the repeating decimal as a variable.
Let:
\[
x = 0.\overline{715}
\]

### Step 2: Multiply by a power of 10 to shift the decimal.
Since "715" is a three-digit repeating block, multiply both sides by \(10^3 = 1000\):
\[
1000x = 715.\overline{715}
\]

### Step 3: Subtract the original equation from this new equation.
Subtract \(x = 0.\overline{715}\) from \(1000x = 715.\overline{715}\):
\[
1000x - x = 715.\overline{715} - 0.\overline{715}
\]
This simplifies to:
\[
999x = 715
\]

### Step 4: Solve for \(x\).
\[
x = \frac{715}{999}
\]

### Step 5: Simplify the fraction.
The greatest common divisor (GCD) of 715 and 999 is 13, so divide both the numerator and denominator by 13:
\[
x = \frac{715 \div 13}{999 \div 13} = \frac{55}{77}
\]

Thus, \(0.\overline{715} = \frac{55}{77}\).

Would you like more details or have any questions about this conversion?

### Related Questions:
1. How would you convert a decimal like \(0.\overline{23}\) into a fraction?
2. What is the method to convert a repeating decimal with more digits, like \(0.\overline{12345}\), into a fraction?
3. Why do repeating decimals always convert into rational numbers (fractions)?
4. How do you calculate the GCD of two numbers to simplify fractions?
5. How does the method differ when the repeating part of a decimal starts after some non-repeating digits?

### Tip:
When converting repeating decimals to fractions, always remember to shift the decimal by a power of 10 that matches the length of the repeating block.

Convert the repeating decimal 0.715 (where 715 repeats indefinitely) into a fraction.

Learn how to convert the repeating decimal 0.715 (with '715' repeating) into a fraction. This guide walks you through step-by-step using algebraic techniques and fraction simplification, suitable for students in Grades 8-10.

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