Indeed, the author conveys the wrong message when implying that only pure numbers have no units. Measurable quantities, as you point out, can also have no units

Indeed, the author conveys the wrong message when implying that only pure numbers have no units. Measurable quantities, as you point out, can also have no units. Another point that throws me off is the Vulcan scientist part. They would need to be using the same numerical base in order to get that number. There might be some base-less representations of numbers, but they are usually restricted to representing integer numbers. The constant could still be represented by a fraction, but there would be no math-neutral way of saying "hey, this here is a fraction/division".