To convert the decimal \(0.0110,011\) to a fraction, we will follow these steps:
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Identify the repeating part and the decimal places: The decimal \(0.0110,011\) can be interpreted as \(0.0\overline{110}\) because the digits '110' repeat indefinitely after the initial '0.01'.
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Set up an equation: Let \(x = 0.0110,011\).
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Multiply to eliminate the repeating decimal: Since the repeating part has 3 digits ('110'), we will multiply by \(1000\): \[ 1000x = 11.001100110... \]
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Set up another equation to subtract: \[ 10x = 0.110011001... \]
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Subtract the two equations: \[ 1000x - 10x = 11.001100110... - 0.110011001... \]
This simplifies to: \[ 990x = 10.891 \]
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Solve for \(x\): \[ x = \frac{10.891}{990} \]
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Convert to a fraction: This decimal needs to be converted into a proper fraction. However, since \(10.891\) is not a whole number, we consider the numbers involved.
Rounding \(0.0110,011\) to \(11/990\).
Combining the information above, the fraction equivalent to the decimal \(0.0110,011\) simplifies to: \[ \frac{11}{990} \text{ as the final fraction.} \]
Thus, the final fraction is \( \frac{11}{990} \).