To describe the relation in sizes of two values to each other, one could use fractions and division. 1 compared to 2, is the same as 1/2 or 1:2, and likewise, when describing 5 compared to 10, you could write 1/2 for clarity/brevity; not using the lowest power of common primes, is just less accurate overall.
But when It comes to less obvious ratios, you are forced to resort to higher numbers. 5/249th's is more precise than saying 1/50th't: larger values provide more precision.
PI is given as the ratio of circumference and diameter. And, given that there are infinite amounts of primes to be found, each adding some 'relative uniqueness', how can we say for sure that there is no prime 'unique' enough to describe the ratio of circumference and diameter precisely, without resorting to decimals?
Knowing that an infinite amount of primes exist, wont they eventually, written as x/large_prime, be able to describe a value less divisible than the ratio of PI? How do we know that there is no such (power of a) prime? When each new prime offer an increasing relative uniqueness.