Zillion has an indeterminate number of zeroes. Despite the popular misconception, zillion actually is not a true number. Rather, zillion is defined as an indeterminately large number.
The first known use of the word zillion is in 1934. A derivation of zillion is zillionaire. Zillionaire refers to a particularly wealthy individual. Another take on the word zillion is gazillion. Gazillion is also used to refer to an indeterminately large number. However, in addition to referencing a particularly large number, gazillion is most often used with at least a hint of jocularity. The most common misconception associated with zillion is that it follows trillion in the order of numbers.