To turn \(8.(3)=8.333...\) into a fraction you should do such steps:
1 step. Set up an equation by representing the repeating decimal with a variable. Using your example, you will let x represent the repeating decimal 8.(3), so you have x=8.333... .
2 step. Identify how many digits are in the repeating pattern, or n digits. Multiply both sides of the equation from Step 1 by \(10^n\) to create a new equation. Again, using your example, you see that the repeating pattern consists of just one digit: 3. Now multiply both sides of the equation by \(10^1 = 10\). Thus, you have \(10x = 10 \cdot 8.333...\) or \(10x = 83.333....\).
3 step. Subtract the equation in Step 1 from the equation in Step 2. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, \(10x-x=83.333...-8.333...\\ 9x=75\).
4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: \(9x = 75\). If you divide both sides by 9, you get \(x=\dfrac{75}{9}\). When simplified, you get that \(x=\dfrac{25}{3}\).
Answer: \(8.(3)=8.333...=\dfrac{25}{3}=8\dfrac{1}{3}\).
