Convert 0.6¯¯¯

Question

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

Answer 1

Let $x=0.6\bar{6}$.

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

$$10x=6.6\bar{6}$$

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

$$10x-x=6.6\bar{6}-0.6\bar{6}$$

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:

$$x=\frac{6÷3}{9÷3}=\frac{2}{3}$$

Thus, the fraction that is equivalent to $0.6\bar{6}$ is $\frac{2}{3}$.