Are there limits to binary

Answer 1

Absolutely. Just as it is impossible to write irrational fractions such as 1/3 in decimal form other than by approximation (such as 0.33 or 0.3333), binary notation has the same problem. When working with floating point values, there's always the chance we'll introduce tiny errors through rounding. We can allocate more memory to improve accuracy, but we must impose limits because memory is a finite resource. Thus all floating point values are an approximation.