Creating a New Number System!

High nerd alert for this post! I haven't done something along these lines for a while. But we're going to be talking conlangs (constructed languages), and, even more specifically within that, number systems for those conlangs.

Quite a while back, I mentioned a language that I was starting to make, Aiyæthron. At some point a bit more recently, I came up with a number system for it. And I don't just mean different words for our numbers, but a somewhat different way of doing numbers.

For starters, this language works in base-8, not base-10. I did that for a few reasons - partly just because I like the idea of base-8 (it divides by two much more nicely), but it also means that 7 is the last digit, and so it does the cool stuff 9 does in our base; and for the people speaking this language (the Aiyædwur), 7 is somewhat of a significant religious number.
If you're not familiar how bases work, it basically (haha) means how many digits you use. We're in base-10, so we use 0123456789. In base-8, though, you only use 01234567. Which means that after 7, you skip straight to 10. After 17, you go to 20. After 77, you have 100. It takes a little bit of getting used to (particularly if you try doing any maths), but hopefully you get the idea.

The next thing different is when you do new words. In English, we have a new word when we get to a hundred, then a thousand, and then every time you multiply by a thousand - which works out to being every comma separator. In Aiyæthron, however, you only have a new word when you can't describe it with the words you already have, without repeating a word (you can't say hundred hundred). In effect, this means that each new word is the square of the previous - so you get up to words for really big numbers quite quickly (as you'll see below).

Then, they do a comma separator after every hundred (two zeroes) rather than every thousand (three zeroes). And how numbers are written out is a little different - it's similar to how it's done in Indonesian, in an additive way. So 23 would be "two tens three". 17 would be "ten seven". So you don't need to know that many numbers to be able to say quite large numbers.

And that's it. That's the only things that separate it from our normal number system - apart from the language itself, of course! Also, a note that I haven't figured out a text/script for this language yet, so it won't be using our English letters and numbers. That's just what I'm using for now so that others can see how it's pronounced etc.

Cah -> One [number]
Dehn -> Two [number]
Fih -> Three
Hohn -> Four
Juh -> Five
Lahn -> Six
Neh -> Seven
Chÿ -> Ten (for us, eight)
Zuht -> Zero

Gÿ -> One hundred [Chÿ x Chÿ, or 64 in base-10] 100
Rÿ ->Ten thousand (our next word would be a thousand) [Gÿ x Gÿ, or 4,096 in base-10] 100,00
Sÿ -> Hundred million (our next word is a million) [Rÿ x Rÿ, or 16,777,216 in base-10] 100,00,00,00
Tÿ -> Ten quadrillion (then billion) [Sÿ x Sÿ, or 281,474,976,710,656 in base-10] 100,00,00,00,00,00,00,00
Thÿ -> Hundred nonillion (and then trillion) [Tÿ x Tÿ, or 79,228,162,514,264,337,593,543,950,336 in base-10] 100,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00

Zhe- -> turns number into ordinal number, i.e. first, second, third, fourth, etc. [e.g. Zhecah, zhedehn, zhefih, zhehohn, zhejuh, zhelahn, zheneh, zhechÿ, etc.]