To turn \(3.(8)=3.888...\) into a fraction you shouls 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 3.(8), so you have x=3.888... .
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: 8. Now multiply both sides of the equation by \(10^1 = 10\). Thus, you have \(10x = 10 \cdot 3.888...\) or \(10x = 38.888....\).
3 step. Subtract the equation in Step One from the equation in Step Two. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, \(10x-x=38.888...-3.888...\\ 9x=35\).
4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: \(9x = 35\). If you divide both sides by 9, you get \(x=\dfrac{35}{9}\). When simplified, you get that \(x=3\dfrac{8}{9}\).
Answer: \(3.(8)=3.888...=3\dfrac{8}{9}\).
