To convert the repeating decimal \(0.93\overline{3}\) (which means 0.933333...) into a simplified fraction, we can follow these steps:
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Let \(x = 0.93\overline{3}\).
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To eliminate the repeating part, multiply both sides by 10 (to shift the decimal point one place): \[ 10x = 9.3\overline{3} \]
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Now, multiply both sides by 10 again: \[ 100x = 93.3\overline{3} \]
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Now, we have the two equations: \[ 10x = 9.3\overline{3} \] \[ 100x = 93.3\overline{3} \]
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Subtract the first equation from the second: \[ 100x - 10x = 93.3\overline{3} - 9.3\overline{3} \] \[ 90x = 84 \]
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Now, solve for \(x\): \[ x = \frac{84}{90} \]
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Simplify the fraction: \[ x = \frac{14}{15} \]
Thus, the simplified fraction of \(0.93\overline{3}\) is \(\frac{14}{15}\).