Question

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

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

Answer 1

To convert the repeating decimal \(0.6\overline{6}\) (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 \(0.6\overline{6}\) is \(\frac{2}{3}\).

Looking at the answer choices provided:

- \(6/5\)
- \(6/10\)
- \(4/5\)
- \(2/3\)

The correct answer is \(\frac{2}{3}\).