Here 'truncating' implies reducing precision of the random numbers and not truncating the series of random numbers. For example, if I have $n$ truly random numbers (drawn from any distribution, e.g., normal, uniform, etc.) with arbitrary precision and I truncate all the numbers so that finally I end up with a set of $n$ numbers, each with exactly 2 digits after the decimal. Can I call this new set of numbers 'random'?
I came up with this question when I was reading about hardware generated random numbers. The Wikipedia article says they generate random numbers by measuring a physical process. But since this measurement has its limitations (measurement error, finite precision, etc) can we call these hardware generated numbers random?