When I tried 2/3 in calculator it shows 0.66666667 same as Quantity A, but in the video Greg choose option A. So, what to do?

It’s testing your knowledge of repeating decimals I guess? One third is 0.3333repeating(with the bar on top of the 3) and two thirds is 0.6666repeating. If you use the calculator you have to realize that it’s rounding in this case. If it asked you which is greater 0.666repeating (with the bar on top) or 0.66666667 you probably would have no problem spotting that 0.66666667 is bigger, right?

The problem with assuming the calculator is exact is that it has to round to a finite amount of digits. So it’s fine for 99.9% of problems, just not ones testing for this specific type of number.