why does 2/3 equal 0.666666666666666667?

The answer has to do with useful utility in solving formulas at or current level of technological reach. Likely the smallest measurable dimension used in lab research is in the field of light travel distance speeds. Scalar multiplied creating speed differential frequencies far beyond the old ideas that science used to believe about light. The yoctosecond is a septillionth of a second. Hence we need to round off the repeating decimals to that place for consistency.