The rumen is the first gut chamber of certain animals called ruminants. Ruminants use microorganisms to ferment and otherwise partially digest cellulose-bearing vegetable matter. Ruminants include cattle, dear, giraffes, antelopes, goats, sheep but also some marsupials. The microorganisms include fungi, bacteria, archaea, ciliates and more.
There’are something like 4 billion ruminants in the world (4 × 10^9), and it is estimated that a litre of rumen fluid contains a quadrillion organisms (10^15).
Obviously the size of the rumen varies greatly by species but the single biggest category of ruminant by headcount is the dairy cow, which has a rumen about 175 L in capacity.
The rumen world population, then, is something in the general vicinity of 700000000000000000000000000, or 7 × 10^26. This could be expressed as 700 septillion, or seven hundred million billion billion.