What is 0.66666666666 as a fraction

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What is 0.66666666666 as a fraction


To turn ?f=0.(6)%3D0.6666.. 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 ?f=10%5En 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 ?f=10%5E1%20%3D%2010. Thus, you have or .

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, ?f=10x x%3D6.666... 0.666...

4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: . If you divide both sides by 9, you get . When simplified, you get that .

Answer: ?f=0.(6)%3D0.666...

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