when using bits to represent fractions of a number, can you create all possible fractions? why or why not?

When using bits to represent fractions of a number, it is not possible to create all possible fractions. This limitation arises because bits represent numbers in a binary system based on powers of two. With a finite number of bits, only fractions that can be expressed as sums of powers of two can be exactly represented (such as 1/2, 1/4, or 3/8). Many fractions, especially those that correspond to repeating or non-terminating binary expansions (like 1/3 or 1/10), cannot be represented exactly with a finite number of bits. The precision and the set of representable fractions are constrained by the number of bits available, forcing approximations for many fractions. Thus, while many fractions can be represented approximately or exactly if they fit the binary power structure within the bit limit, not all possible fractions can be represented due to the finite and binary nature of the representation system.