Roman numerals

The **Roman numerals** are a set of numerals used by the Romans to express numbers.

## Definition

The Roman numerals are defined by the following steps:

1. Split the number into their place values. Example: 1023 = 1000 + 20 + 3.
2. Arrange the parts from thousands to ones. 1000 + 20 + 3.
3. Convert the parts to Roman Numerals according to this chart:

Example: 1000 + 20 + 3 = M + XX + III

Therefore, 1023 = MXXIII.

## Larger Numbers

According to 4, 40 and 400, 4000 should be 5000-1000. But there isn't a Roman Numeral for 5000. Here are a couple Roman Numeral variations for larger numbers:

### Apostrophus

The apostrophus is defined as follows:

C|Ɔ is 1000. CC|ƆƆ is 10000, and CCC|ƆƆƆ is 100000. Think of C and Ɔ like parentheses. The number of CƆ's is the number of zeros after 100, also raising the previous by a factor of ten.

In this system, there is no D or M, or subtractive definitions for larger numbers. so 400 is CCCC instead of CD. You're just repeating numbers in an efficient way.

With the apostrophus, you can write any number in Roman Numerals. Example: 123456 = 100000 + 20000 + 3000 + 400 + 50 + 6.

100000 = CCC|ƆƆƆ

20000 = CC|ƆƆCC|ƆƆ

3000 = C|ƆC|ƆC|Ɔ

400 = CCCC

50 = L

6 = VI

### Vinculum

Instead of using apostrophi, which could make a number very difficult to represent, we could scale a number by a factor of 1000 by drawing a line above the numeral, if the result is above or equal to 4,000. Therefore, 3,000 would be MMM, but 4,000 would be I̅V̅. 5,000 is V̅. 10,000 is X̅, and 100,000 is C̅. 1,000,000 is M̅. This variant is much simpler than the above and therefore is preferred by many.

100000 = C̅

20000 = X̅X̅

3000 = MMM

400 = CD

50 = L

6 = VI

Therefore, 123456 = C̅X̅X̅MMMCDLVI.

## Into different bases

In the base analyst community, Roman numerals have been converted into different even number bases as decimal is not preferred by some. The values of the letters have been adjusted according to powers of the new base. The base indicators, such as the Humphrey point, are still used to distiguish the number from decimal.

Below is a table of values of roman numerals for decimal and dozenal, as well as other even bases

b

{\displaystyle b}

:

Subtractive numerals such as 4 = IV (in decimal) also applies to other bases as well. They are applied to digits with value ranging from

b
4

1

{\displaystyle \frac{b}{4}+1}

to

b
2

−
1

{\displaystyle \frac{b}{2}-1}

as well as

3
b

4

1

{\displaystyle \frac{3b}{4}+1}

to

3
b

2

−
1

{\displaystyle \frac{3b}{2}-1}

.

That is, for dozenal roman numerals, 4 is written as IIV; since

b
4

# 1
4

{\displaystyle \frac{b}{4}+1=4}

when

# b
12

{\displaystyle b = 12 }

. The same rule would apply to 5,  and , being written as IV;, IIX; and IX; respectively.

This would get complicated for large bases, as many symbols are required for small numbers. This, however could be solved with defining new letters as other round values. (For instance, the decimal number 15 in sexagesimal roman numerals would be represented as IIIIIIIIIIIIIII, which could be simplified as AIIIII, defining A as the new symbol for ten.) No proposal for such has been known yet.

Numeral Sets