Convert 0.6¯¯¯

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

1 answer

Let \( x = 0.6\overline{6} \).

To eliminate the repeating decimal, we can multiply \( x \) by 10 (since the repeat is one digit long) to shift the decimal point:

\[ 10x = 6.6\overline{6} \]

Now, we can set up the following equation by subtracting the original \( x \) from this equation:

\[ 10x - x = 6.6\overline{6} - 0.6\overline{6} \]

This simplifies to:

\[ 9x = 6 \]

Now, we can solve for \( x \):

\[ x = \frac{6}{9} \]

Next, we reduce the fraction to its lowest terms. The greatest common divisor of 6 and 9 is 3:

\[ x = \frac{6 \div 3}{9 \div 3} = \frac{2}{3} \]

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