Roman Numerals, Forming Roman Numerals

Roman Numerals, Forming Roman Numerals

Roman Numerals

Roman numerals are represented by seven different letters: I, V, X, L, C, D and M, which represent the numbers 1, 5, 10, 50, 100, 500 and 1000, respectively.

Roman Numerals Chart

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

These seven letters are used to make thousands of numbers. For example, the Roman numeral for three is written as 'III', just three one's added together. The numeral thirteen is written as XIII, which is simply X + III. If we take this a step further, the number twenty-eight is written as XXVIII, which when broken down looks like XX + V + III.
Roman numerals are usually written largest to smallest from left to right. However, this is not always the case. The Romans didn’t like four of the same numerals written in a row, so they developed a system of subtraction.
The Roman numeral for three is written as ‘III’, however, the numeral for four is not ‘IIII’. Instead we use the subtractive principle. The number four is written as ‘IV’, the numerals for one and five. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as ‘IX’. There are six instances where subtraction is used:
i.            I can be placed before V (5) and X (10) to make 4 and 9.
ii.            X can be placed before L (50) and C (100) to make 40 and 90.
iii.            C can be placed before D (500) and M (1000) to make 400 and 900.
The number 1994 is a great example of these rules. It is represented by the Roman numerals MCMXCIV. If we break it down, then M = 1000, CM = 900, XC = 90 and IV = 4.

How to Form Roman Numerals?

There are Four Basic Principles for Reading and Writing Roman Numerals:

1. A letter can only be repeated three times (e.g. XXX = 30, CC = 200, MMM = 3000, etc.). V, L and D cannot be repeated.
2. If one or more letters are placed after another letter of greater value, add that value.
VI = 6 (5 + 1 = 6)
LXX = 70 (50 + 10 + 10 = 70)
MCC = 1200 (1000 + 100 + 100 = 1200)
3. If a letter is placed before another letter of greater value, subtract that value.
IV = 4 (5 – 1 = 4)
XC = 90 (100 – 10 = 90)
CM = 900 (1000 – 100 = 900)

Several Rules Apply for Subtracting Amounts from Roman Numerals:

1. Only subtract powers of ten (I, X or C, but not V or L)
For 95, do NOT write VC (100 – 5).
DO write XCV (XC + V or 90 + 5)
2. Only subtract one number from another.
For 13, do NOT write IIXV (15 – 1 – 1).
DO write XIII (X + I + I + I or 10 + 3)
3. Do not subtract a number from one that is more than 10 times greater (that is, you can subtract 1 from 10 [IX] but not 1 from 20—there is no such number as IXX.)
For 99, do NOT write IC (C – I or 100 – 1).
DO write XCIX (XC + IX or 90 + 9)
4. A bar placed on top of a letter or string of letters increases the numeral's value by 1000 times.
X = 10, bar on X = 10,000