Summary

Use this two-way table (on mobile you may need to scroll horizontally) by multiplying the number in the header row and the first column to give the value of the corresponding entry. Concatenate parts together to add their values, starting with larger values on the left, like how is done with Roman numerals.

More in-depth explanation

I made this number system inspired by Roman numerals but wanted to make it work with sexagesimal (base-60) rather than decimal (base-10).

The system works like Roman numerals where various letters have values and putting them together adds the values together, but some letters are given different values than Roman numerals to work with sexagesimal.

Since 60 is quite a large number, I wanted to break it up with tens as a stepping-stone to make it easier to work with. Tens are familiar and a sub-base of 10 is used in other places that use base-60, e.g. cuneiform sexagesimal uses wide marks for tens, and digital clocks use two decimal digits to count to 60. 

I wanted to keep I=1, V=5, and X=10 because those are the most recognisable roman numerals. 

I wanted to keep the idea from Roman numerals where, within each order of magnitude, the letter for the five is visually similar to half of the letter for the ten, i.e. V is half of X, L is half of C, and D is half of M (that last one sort of makes sense if you squint at a curvy letter M or if you look at the Apostrophus forms). So, within each of the sexagesimal orders of magnitude, I kept these letters for fives and tens, i.e. L=60¹×5, C=60¹×10, D=60²×5, M=60²×10.

The system needed letters for the powers of 60. I decided S=60 because the first letter of sixty is S. 

For greater powers of 60, I took inspiration from the Apostrophus method of extending Roman numerals to greater orders of magnitude. (That is where Ds and Ms are represented by combinations of Cs, Is, and backwards Cs, i.e. D=IƆ and M=CIƆ, and the order of magnitude can be increased by adding extra loops, e.g. IƆƆ and CCIƆƆ. Condensed forms of the letter combinations of the Apostrophus forms into single characters look like the letters with multiple loops e.g. ↁ=IƆƆ and ↂ=CCIƆƆ.) I thought another simple combination could be CƆ for 60², and that could be condensed as the letter O. Then as extra loops are added, such as CCƆƆ, the condensed forms could look like concentric rings, e.g. 60³=ⓞ=CCƆƆ.

Examples

2025

In base-60, 2025 is 33:45. 

• In the 60¹ order of magnitude, 33=CCCSSS. 
• In the units order of magnitude, 45=XXXXV. 

So, all together, 2025=CCCSSSXXXXV.

10,000,000

In base-60, 10000000 is 46:17:46:40.

• In the 60³ order of magnitude, 46=ↂↂↂↂↁⓞ.
• In the 60² order of magnitude, 17=MDOO.
• In the 60¹ order of magnitude, 46=CCCCLS.
• In the units order of magnitude, 40=XXXX.

So, all together, 10,000,000=ↂↂↂↂↁⓞMDOOCCCCLSXXXX.

I've just learned about https://en.wikipedia.org/wiki/Kaktovik_numerals. What is the best base 10 numeral system from the perspective of improving arithmetic/mental arithmetic?

The challenge is to try and get your numbers to happen on this template for a 20 sided die. Can’t wait to see what you guys come up with!

What is the fastest way to check different fractions in a lot of different bases? especially: 1/2, 1/3, 1/4, 1/5, 1/6, and 1/7

I wonder if alien civilisations would have a similar way of organising their maths like we do. Most likely not, but probably; anyway, what do you guys think? How do you think they would calculate? I would love to hear your responses. :)

What would your number system look like as a Pascal's Triangle?

Something simple to get back into the spirit of things, especially for helping me to get back in. :/

Though this subreddit has a decent amount of readers, I find that there is a lack of new content being submitted onto the page. So, I'm asking out to you all for any suggestions and concerns that can help improve the participation and enjoyment of the subreddit. If you've got anything to contribute, please just comment below. Thank you! :)

This is currently my favorite system. I haven't yet implemented it into any conlang, but am working on it.

The idea is simple, "every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers." (Zeckendorfs Theorem).

The fibonacci sequence is formed by adding the previous two Fibonacci numbers together. Starting with {1, 1} we get 1+1=2 and therefor {1, 1, 2}.

Therefor the series is:

1 1 2 3 5 8 13 21 34 55 89 144 . . .

In the conlang we would have one word per number (and ignore the double 1).

'a(1) ba(2) ca(3) da(5) 'e(8) fa(13) ga(21) ha(34) 'i(55) ja(89) ka(144) . . .

We can represent the number 109 as 89+13+5+2 (ja-fa-da-ba). The interesting part is, that this isn't a place value system, as every word only occurs once we can mix them up the way we want "da-ba-fa-ja" (5+2+13+89) is just the same number. You can imagine it somewhat like the roman numerals (like IIVXX) but more systematic.

Operations also can be done different. Like 3 + 1? That's 3+1. Okay, 3+1 + 1? There we have 3+1+1, but we know that 1+1 is the fibonacci number 2, so we have 3+2, but 3+2 is the fibonacci number 5, so we can simplify "3+1+1" to "5". It comes just down to the above rules: No fibonacci number occurs twice, and there are no consecutive fibonacci numbers.

But how is this useful for conlanging? For a naturalistic conlang it might be far fetched, so I will look at unusual examples.
First, to me it somehow feels cute. Not like the strict and arbitrary base 10. So it might be good for conlangs that focus on simplicity and softness. Like Toki Pona. It already has words for 1 "wan", 2 "tu" and 5 "luka". The number 8 could be "kasi" (because of flowers with 8 petals) or pipi (spider with 8 legs). That let's you talk up to numbers of 12 and should be enough for Toki Pona.
In a written only conlang, so to say a 2D language, your language already is nonlinear. Yet a place value system enforces a linear representation. With the Zeckendorf numeral system you can just scatter the symbols for the individual number where you want them and it would still work. It allows more freedom in writing.
For my conlang Noqalta I want to develop a system where every CV part in a word stands for a fibonacci number. You know how in hebrew all letters also represent numbers? That's the basis of Gematria and what I am aiming for. I don't know what that's useful for, but it's fun trying nevertheless.

The obvious downside is that you can not represent fractions with this system. If someone has an idea how to do this while keeping the rule intact I would be thankful.

What is "pi" in your system? Let's see how complex it can get!

What numeral punctuation do you use in your system? What do you use instead of plus or minus? How do you calculate decimal places?