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To turn in a fraction that you must do these steps:1 step. To establish an equation that represents the repeating decimal with a variable. Using your example, you are going to let x represent the repeating decimal 0.(6), so has x=0.666... .2 step. Identify the number of digits in the repeating pattern, or of n digits. Multiplying both sides of the equation in Step 1 to create a new equation. Again, using your example, you can see that the repeating pattern consists of a single digit: 6. Now multiply both sides of the equation . Therefore, you have or .3 step. Subtract the equation in Step 1 of equation in Step 2. Notice that when we subtract the equations, our pattern of repeat falls. Therefore, .4 step. You now have an equation that you can solve for x and simplify, to the extent possible, the use of x as a fraction: . If you divide both sides by 9, is obtained . When simplified, you get that .Answer: .