# Subtractive Principle

## Learn the Roman Numeral Subtractive Principle

The Romans didn’t like to use more than three identical numerals sequentially to represent a number, so they established a subtractive principle.

The subtractive principle, applies to the numbers 4, 9, 40, 90, 400 and 900 only.

To explain how this works we will use the number ‘4’ as an example. To correctly write the number ‘4’ as a numeral we do the following:

- Take the numeral for 5 (V)
- Subtract 1 (I) to make the number 4

The subtraction is made by:

- Placing the ‘I’ before the ‘V’ to make; ‘IV’.
- So ‘4’ = ‘IV’, and not ‘IIII’

The same principle applies to all the numbers in the first column of the following table, that demonstrates the correct way to write the numerals that the principle is applied too.

Number | Subtractive | Incorrect Numerals | Correct Numerals |
---|---|---|---|

4 | 5 - 1 | IIII | IV |

9 | 10 - 1 | VIIII | IX |

40 | 50 - 10 | XXXX | XL |

90 | 90 - 10 | LXXXX | XC |

400 | 500 - 100 | CCCC | CD |

900 | 1000 - 100 | DCCCC | CM |

- I is placed before V (5) and X (10) to make 4 and 9.
- X is placed before L (50) and C (100) to make 40 and 90.
- C is placed before D (500) and M (1000) to make 400 and 900.

Knowing this principle is very important, especially in circumstances involving tattoos and important documents. For example, the correct way for writing the year 1999 in Roman numerals would be:

**MCMXCIX**

= 1000 + 900 + 90 + 9

And not:

**MDCCCCLXXXXVIIII**

= 1000 + 500 + 100 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 10 + 5 + 1 + 1 + 1 + 1

You wouldn’t want the incorrect numerals as a permanent decoration on your body. Neither would you want to make this mistake in an important text. Sadly there are several websites that provide **incorrect Roman numeral conversations**, but feel rest assured, our converters always provide 100% correct results.