Drawer I: the ones
The common ones. 1e3 through 1e30, each with its own irregular Latin root.
Drawer II: the tens
The main tens-roots from 1e33 onward. Everything in between reads additively: a tens-root plus a whole Drawer I word, like vigintitrillion (1e72), which is viginti (twenty) plus trillion, rather than mashing three prefixes into one. The lookup tool above will name any of them.
Drawer III: the hundreds
Past 1e303, the system adds a hundreds prefix. Shown here in steps of one hundred. This construction is deliberately additive rather than a straight prefix mash-up, which is what lets 103 (centitrillion) and 300 (trecentillion) stay clearly distinct instead of colliding into the same word.
Drawer IV: the blocks
Past 1e3000 (n = 999), the naming keeps going by reusing ten dedicated "block" words, myri, million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, each one a thousand times bigger than the last. So the thousandth illion is myriillion, the millionth is millionillion, the billionth is billionillion, all the way out to 1e33 (roughly the nonillionth illion). Past that, a second dedicated pair, "vasti" and "nulla", takes over and chains indefinitely, the same trick one level up.
Drawer V: the repetition
Once the ten block-words above are exhausted, "vasti" and "nulla" chain the whole system into itself indefinitely, the same recursive trick, just one level higher. The lookup tool above will name anything in this range too, no matter how far you push it.