# Roman numerals

Roman numerals are a way of writing numbers that originated in ancient Rome. Roman numerals are based on symbols that represent a certain value, that are then used in combination to represent other values. In Roman numerals:

- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000

Roman numerals are often used on clock faces as the hours 1 through 12. Specifically, I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII. They are also used in the names of monarchs and popes (Queen Elizabeth II), to indicate names across generations (Michael Smith IV), building construction years, sequels to movies, games, etc., sections in outlines, and more.

### How to write Roman numerals

The values and symbols shown above can be written, following certain rules, to represent different values. These rules mainly exist through convention, as there is no universally accepted standard. Some of the values may be more intuitive than others, for example III = 3, while others, such as IV = 4, may not be as obvious. To write Roman numerals, use the following rules:

- Symbols should not be used more than three times in a row
- When a symbol that is larger follows a smaller symbol, subtract the smaller symbol's value from that of the larger symbol
- When a symbol is larger than or equal to the following symbol, add the value of the symbols

Examples

XCIV:

Individually, X = 10, C = 100, I = 1, and V = 5. If we were to just add these up, we would get 116, which is incorrect. Following the rules above however,

XC = 100 - 10 = 90

IV = 5 - 1 = 4

XC + IV = 90 + 4 = 94

MMCDVIII:

Individually, M = 1000, C = 100, D = 500, V = 5, I = 1. Adding this up would give us 2,608, but this is incorrect. Following the rules described above,

MM = 1000 + 1000

CD = 500 - 100 = 400

VIII = 5 + 1 + 1 + 1 = 8

MM + CD + VIII = 2000 + 400 + 8 = 2408

Note that the values for MM and VIII are the same in the first example; it's just the CD that changes from 600 to 400 since C is subtracted from D based on the position of the symbols, not added.

For even larger Roman numerals, we can add a bar over the letter used to form a new symbol that indicates multiplication by 1,000, similar to the "k" when talking about thousands.

- I = 1,000
- V = 5,000
- X = 10,000
- L = 50,000
- C = 100,000
- D = 500,000
- M = 1000,000