Question

What is 0.66666666666 as a fraction

Answer 1

To turn $0.(6)=0.6666...$ 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 0.(6), so you have x=0.666... .

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: 6. Now multiply both sides of the equation by $10^1 = 10$. Thus, you have $10x = 10 \cdot 0.666...$ or $10x = 6.666....$.

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, $10x-x=6.666...-0.666...\\ 9x=6$.

4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: $9x = 6$. If you divide both sides by 9, you get $x=\dfrac{6}{9}$. When simplified, you get that $x=\dfrac{2}{3}$.

Answer: $0.(6)=0.666... =\dfrac{2}{3}$.

Answer 2

 For this case we hace the following expression:
 0.66666666
 We observe that this expression represents two thirds of the unity that is one.
 Therefore, we can rewrite the decimal expression as a fraction.
 In this case, the fraction is given by:
 $\frac{2}{3}$
 Answer:
 0.66666666 as a fraction is:
 $\frac{2}{3}$