Having no guidance but my textbook, which explains basic concepts, but leaves to more in depth stuff to the teacher (of which I have none), I turn yet again to the forums to help me with the following problem.

converted to a fraction.

Now, knowing how to convert a decimal if there are TWO repeating numbers directly after the decimal point, but not having any explanation of what to do if there is one non-repeating number followed by a repeating number, I figured I'd follow the same line

of reasoning.

etc, but I feel like this is the wrong path to be going down. I know it works for 2 repeating numbers after the decimal point, but what do I do when there's one number after the point followed by a repeating number?