Question

Rewrite as a simplified fraction.

\[\large{0.6\overline{7} = {?}}\]

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's call the unknown value of the fraction $x$. We can write the decimal part as a fraction by putting the digit $7$ over $9$ since there is a repeating block of one digit. So, we have $0.6\overline{7}=\frac{6}{10}+\frac{7}{90}$. Simplifying, we get $\frac{6}{10}+\frac{7}{90}=\frac{54}{90}+\frac{7}{90}$. Combining the fractions, we have $\frac{54+7}{90}$. Adding the numerators, we have $\frac{61}{90}$. Therefore, the simplified fraction is $\boxed{\frac{61}{90}}$.