- Is there a similar theorem to the fundamental theorem of arithmetic that applies to all rational numbers?
The fundamental theorem of arithmetic applies to prime factorizations of whole numbers. Can this theorem also correctly be invoked for all rational numbers? For example, if we take the number 3.25, it can be expressed as 13/4. This can be expressed as 13/2 x 1/2. This cannot be broken down further into smaller rational numbers, so these two rational factors are unique. So, I guess my question is, as long as the number we are factoring is a rational number, then there is only one unique factorization of rational numbers that it can be broken down into? So in a way the fundamental theorem of arithmetic applies to rational numbers too?