What is 0.7 (with a line over the 7) as a fraction in simplest form?

Any repeating pattern of numbers is a rational number.

Let x=.7777 ..., then 10x=7.7777 ... getting the difference you find:

9x=7

x=7/9 so that is the rational number which produces the repeating pattern of 0.7777 ...

7/9 is the correct answer.