Question

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

Answer 1

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 \( \frac{2}{3} \).