Session 4: Roman Numerals – Definition, Rules, Chart, Conversion and Examples

We usually write numbers in a notation called Hindu-Arabic numbers, a set of 10 symbols- 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. These numbers originated in India and were later adopted in the Middle East and Europe. But before that, in Western culture, numbers were written in the Roman style. In fact, in a lot of formal documents, we still use roman numerals.

What are Roman Numerals?

The main theory about the origin of roman numerals is that they were invented by shepherds, who counted their flocks by marking notches on their wooden sticks. When counting their sheep, a shepherd would mark four notches and then on the fifth one; they would cut a diagonal notch, in pretty much the same way as a tally system. But instead of striking through the preceding notches, they just used the diagonal to turn a “/” notch into “V.” A strike-through marked every tenth notch, so it looked like an “X.” It is believed that this method of record-keeping was used by Italian shepherds well into the 19th  Century.

In the Roman number system, each symbol has a specific value. There is no way to show place value meaning that a numeric symbol represents a particular value no matter where it is placed. This is very different from our Hindu- Arabic system. The 6 in “64” represents sixty in our number system, but the 6 in “689” represents six hundred. In roman numerals, that’s not true. An “X” always represents ten, no matter where in the number it is placed.

Roman Numeral Symbols

Modern Roman numerals use seven letters to represent different numbers.

• “I” stands for 1. 
• “V” stands for 5. 
• “X” stands for 10. 
• “L” stands for 50. 
• “C” stands for 100. 
• “D” stands for 500. 
• “M” stands for 1000. 

These seven letters are used in different ways to make all the numbers.

Easy Way to Remember Roman Numerals

My Dear Cat Loves Xtra Vitamins Intensely is a mnemonic that many people use to remember the roman numerals. Here, the bold letters represent roman numerals in descending order.

However, writing roman numerals is not that simple. It follows several rules.

Rules for Formation of Roman Numerals

Rule 1: When a symbol appears two or more times in a group- such as III or XXX– they are added together. Thus, III represents 3, and XXX represents 30.

Note: Only symbols for I,X,C and M can be repeated.

Rule 2: When a symbol of a smaller value succeeds a symbol, it is added to its successor.

I follows V so it’s added, so VI=5+1=6.

I follows X so it’s added, so XI=10+1=11.

X follows L so it’s added, so LX=50+10=60.

Rule 3: When a symbol of a larger value succeeds a symbol, it is subtracted from its successor.

I precedes V so it’s subtracted, so IV=5–1=4.

I precedes X so it’s subtracted, so IX=10–1=9.

X precedes L so it’s subtracted, so XL=50–10=40.

Note: Only I,X and C can be used as subtractive numerals.

Rule 4: When a symbol of a smaller number is placed between two symbols of greater value, then subtract from the number represented by the symbol that follows it immediately.

Rule 5: If a horizontal line is drawn over the symbols or digits of Roman numerals, then the value of the numerals becomes 1000 times.

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Roman Numerals Chart

The numerals 1-9, 10,20…,90, 100,200…..500…1000 can be written in roman numerals using the above rules as shown in the table.

Roman Numerals From 1 to 10

Hindu-Arabic Numeral	Roman Numeral	Hindu-Arabic Numeral	Roman Numeral
1	I	6	VI
2	II	7	VII
3	III	8	VIII
4	IV	9	IX
5	V	10	X

Roman Numerals From 1 to 100

Hindu-Arabic numerals to Roman numerals Conversion

To convert a Hindu-Arabic number to Roman Numeral, we write the number in expanded form, followed by their respective roman letter and add/subtract them. Thus, we have

Roman numerals to Hindu-Arabic numerals Conversion

To convert roman numerals to numbers, we split the roman numeral into single letters, write their numerical value and add/subtract them. Thus, we have 

MATCHING ROMAN NUMERALS

Match each of the following Roman numerals to their Hindu-Arabic equivalent.

Roman Numerals – Examples

Example 1 

Write the Roman numerals for:

i. 12

ii. 65

iii. 269

iv. 531

Example 2

Write the Roman numerals for:

i. 738

ii. 920

iii. 3354

 Remember this!

Seven Roman symbols with their corresponding values in the Indian system are: 

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

• When a symbol appears two or more times in a group, they are added together. 
• When a symbol is succeeded by a symbol of a smaller value, then it is added to its successor. 
• When a symbol is succeeded by a symbol of a larger value, it is subtracted from its successor. 
• When a symbol of a smaller number is placed between two symbols of greater value, then subtract from the number represented by the symbol that follows it immediately. 
• If a horizontal line is drawn over the symbols or digits of Roman numerals, then the value of the numerals becomes 1000 times.