Is $$ 0 . \overline{7} $$ a rational number? A. No, because the digit 7 is not repeating. B. No, because the digit 7 is repeating. C. Yes, because the digit 7 is not repeating. D. Yes, because the digit 7 is repeating.

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Let $$ x = 0.\overline{7} $$. This represents an infinite repeating decimal where the digit 7 repeats.

1. Multiply both sides of the equation by 10:
   $$
   10x = 7.\overline{7}
   $$

2. Subtract the original equation from this new equation:
   $$
   10x - x = 7.\overline{7} - 0.\overline{7}
   $$
   This simplifies to:
   $$
   9x = 7
   $$

3. Solve for $$ x $$ by dividing both sides by 9:
   $$
   x = \frac{7}{9}
   $$

Since $$ \frac{7}{9} $$ is a ratio of two integers, $$ 0.\overline{7} $$ is a rational number.

Thus, the correct answer is:

D. Yes, because the digit 7 is repeating.
$$ 0.\overline{7} $$ is a rational number because it can be expressed as the fraction $$ \frac{7}{9} $$.

Is \( 0 . \overline{7} \) a rational number? A. No, because the digit 7 is not repeating. B. No, because the digit 7 is repeating. C. Yes, because the digit 7 is not repeating. D. Yes, because the digit 7 is repeating.

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