To solve the problem of converting the fraction $\frac{2}{3}$ into a decimal:

1. Division Method: Divide the numerator (2) by the denominator (3). $2 \div 3 = 0.6666\ldots$ This results in a repeating decimal of 0.666..., which can be written as $0.\overline{6}$.

2. Conclusion: The correct answer among the options provided is $0.\overline{6}$.

Would you like further details or have any additional questions?

Here are some related questions to consider:

1. How do you convert a repeating decimal back into a fraction?
2. What are the steps to convert any fraction to a decimal?
3. Can you explain why some fractions result in terminating decimals while others do not?
4. What is the significance of the bar notation over a decimal digit?
5. How would the result change if the fraction were $\frac{3}{2}$ instead of $\frac{2}{3}$?

Tip: Always double-check if the decimal is terminating or repeating when converting fractions, as this can impact your final answer.