Final answer:
To convert 66.6% recurring to a fraction, set it as x = 0.6666..., multiply by 10 to get 10x = 6.6666..., subtract the original to get 9x = 6, and simplify to get x = 2/3, which is the fraction form of the recurring percentage.
Step-by-step explanation:
To convert 66.6% recurring into a fraction, we can set it as an algebraic equation since a recurring decimal is a number that repeats infinitely. Let's define x as 0.6666... (recurring). To solve for x, we multiply it by a power of 10 that moves the decimal point to the right just before the repeating digits, which in this case is 10x since our decimal repeats every digit:
10x = 6.6666... (repeating)
Now, we subtract the original equation (x = 0.6666...) from this new equation to get rid of the repeating decimals:
10x - x = 6.6666... - 0.6666...
9x = 6
Divide both sides by 9 to solve for x:
x = 6/9
Now, we simplify the fraction by dividing both the numerator and the denominator by 3:
x = 2/3
Therefore, 66.6% recurring as a fraction is 2/3.