How do i change a recurring decimal into a fraction?

Let's take 0.666... as an example. In this case we can say x = 0. 666... The next step is to multiply both sides of the equation by 10 so that you end up with 10x = 6.666... Now that we have these 2 equations it is possible to eliminate the recurring part of the decimal as we can subtract x from 10x to end up with 9x = 6. The final part is to divide both sides of the equation such that we have x on its own on the left hand side, leaving us with x = 6/9 which can be simplified to x = 2/3.