Which rational number equals 0 point 6 with bar over 6?

Question

Group of answer choices
6/5
6/10
4/5
2/3

Answer 1

To convert the repeating decimal $0.6\bar{6}$ (which means $0.666...$) into a rational number, we can use the following method:

Let $x=0.666...$.

Then, multiplying both sides of the equation by 10 gives us:

$$10x=6.666...$$

Now, we can subtract the first equation from the second:

$$10x-x=6.666...-0.666...$$ $$9x=6$$

Dividing both sides by 9 gives:

$$x=\frac{6}{9}=\frac{2}{3}$$

So, the rational number that equals $0.6\bar{6}$ is $\frac{2}{3}$.

Looking at the answer choices provided:

• $6/5$
• $6/10$
• $4/5$
• $2/3$

The correct answer is $\frac{2}{3}$.