$$$0.666666666666666$$$ to fraction

First, convert the repeating part $$$0.666666666666666$$$ to a fraction.

Let $$$x = 0.666666666666666$$$.

Multiply both sides by $$$10$$$ raised to $$$1$$$ (number of digits to repeat), i.e. $$$10^{1} = 10$$$:

$$$10 x = 6.666666666666666$$$

Subtract the previous equation from the last one:

$$$9 x = 6$$$

Thus, $$$x = \frac{6}{9}$$$.

Since the greatest common divisor of the numerator and the denominator equals $$$3$$$, we can write that $$$\frac{6}{9} = \frac{2\cdot {\color{red}3}}{3\cdot {\color{red}3}}$$$.

Therefore, $$$0.666666666666666 = \frac{2}{3}$$$.

Don't forget about the non-repeating part $$$0$$$.

Since the integer part equals $$$0$$$, we don't add anything. This means that we won't get a mixed number, just a proper fraction.

$$$0.666666666666666 = \frac{2}{3}$$$A