Algebra-1

Question Analysis
This question tests the student's ability to convert a repeating decimal into a fraction. The student must use algebraic manipulation to express the repeating decimal as a fraction.

Key Concept Explanation
Repeating decimals can be expressed as fractions by setting up an equation and solving for the repeating part. This involves multiplying the repeating decimal by a power of 10 to shift the decimal point and then subtracting the original repeating decimal to eliminate the repeating part.

Step-by-step Solution
1. Let .
2. Multiply both sides by 10 to shift the decimal point: .
3. Subtract the original equation from this new equation: