Convert 0.6¯¯¯ to a fraction, reduced to lowest terms.(1 point) The fraction that is equivalent to 0.6¯¯¯ is

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To convert the repeating decimal \( 0.6\overline{6} \) (which represents \( 0.6666\ldots \)) to a fraction, we can follow these steps:

  1. Let \( x = 0.6666\ldots \).

  2. Multiply both sides of the equation by 10 to shift the decimal point: \[ 10x = 6.6666\ldots \]

  3. Now, subtract the original equation from this new equation: \[ 10x - x = 6.6666\ldots - 0.6666\ldots \]

    This simplifies to: \[ 9x = 6 \]

  4. Now, solve for \( x \): \[ x = \frac{6}{9} \]

  5. Reduce the fraction to its lowest terms: \[ \frac{6}{9} = \frac{2}{3} \]

Thus, the fraction that is equivalent to \( 0.6\overline{6} \) is \( \frac{2}{3} \).

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