Question

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Explanation:

Step1: Define the repeating decimal

Let \( x = 0.\overline{92} \), which means \( x = 0.929292\ldots \)

Step2: Multiply by 100 to shift decimals

Multiply both sides by 100: \( 100x = 100\times0.929292\ldots = 92.929292\ldots \)

Step3: Subtract the original equation

Subtract \( x \) from \( 100x \): \( 100x - x = 92.9292\ldots - 0.9292\ldots \)
Simplify: \( 99x = 92 \)

Step4: Solve for x

Divide both sides by 99: \( x = \frac{92}{99} \)

Answer:

\(\frac{92}{99}\)