Which simplified fraction is equal to 0.17 (7 repeating)

So here, I would first multiply 0.17777 ... (Assume that that's x) by 10, then you get

10x = 1.777777 ...

And then subtract x from 10x and then you get 1.6.

So that means that

10x - x = 9x

and 1.7777 ... - 0.17777 ... = 1.6

So now to solve for x, divide both sides by 9

To get 1.6/9 = x

Or 16/90 = x

Or 8/45 = x

(That explanation made no sense)