Answer:
[tex]\frac{59}{300}[/tex]
Step-by-step explanation:
Recall that [tex]\frac{x}{9}[/tex] returns the decimal [tex]0.\overline{x}[/tex]. In this case, we only want the 6 repeating. We can achieve this by finding the fraction excluding the 6 and then adding the repeating fraction with the 6.
0.19 as a fraction is simply [tex]\frac{19}{100}[/tex]
[tex]\frac{6}{9}[/tex] returns a repeating digit 6. However, we would like the 6 to be in the thousands place. Since it's already in the tenth place, we will divide the fraction by 100 to put it in the thousands place: [tex]\frac{6}{9}\cdot \frac{1}{100}=\frac{6}{900}[/tex]
Adding these two fractions, we get:
[tex]\frac{6}{900}+\frac{19}{100}=\frac{6}{900}+\frac{171}{900}=\frac{177}{900}=\boxed{\frac{59}{300}}[/tex]
