What Are Roman Numerals?
Roman numerals are an ancient numeral system that originated in Rome. Roman numerals employ letters from the Latin alphabet to represent numerical values. Although the use of Roman numerals is very limited in today’s world, there are still a few instances where we can spot Roman numerals.
For instance, numbering of chapters in a book, on the face of a clock, to represent grades in schools like Grade I or Grade VIII, titles of global sport events like Winter and Summer Olympics, or the National Football League. We can also identify Roman numerals in the names and titles of monarchs around the world.
How to Write Numbers as Roman Numerals?
The Roman numeral system comprises a seven letter method to represent numbers. Several combinations of these seven letters are used to represent numbers in the form of Roman numerals.
The numerals are either written as uppercase or lowercase letters as per the requirement.
Roman Numeral Forms
Numbers can be written in Roman numerals using:
1. Additive Form
In a combination of Roman numerals, if a numeral or a combination of numerals is ‘equal to’ or ‘smaller than’ the preceding numeral,
the values of the numerals are added together.
Let’s take a look at a couple of examples: VI and XX
In VI, I is smaller than V.
So we will add:
I → 1
V → 5
Hence, VI → (1 + 5) = 6
In XX, same numerals, so XX → 10 + 10 = 20.
2. Subtractive Form
In a combination of Roman numerals, if a numeral is ‘greater than’ its preceding numeral, the values of the numerals are subtracted.
Let’s take a look at an example of the subtractive form: IV
Here, V is greater than I.
So we will subtract:
Hence, IV → (5 – 1) = 4.
IX Roman Numeral in Numbers
Let’s take a look at the Roman numeral, IX. Here, I, the smaller numeral precedes X, the greater numeral. So, on applying the subtractive form:
I → 1
X → 10
Hence, IX → (10 – 1) = 9.
Roman Numeral Chart
Here is a chart of Roman numerals for numbers 1 to 50.
A number can be written as Roman numerals using both additive and subtractive forms, however, as a standard we use the notations shown in the chart.
For example: The number 4 is represented as:
IIII using the additive form, and IV using the subtractive form. However, as a usual standard we use IV to represent the number 4 in Roman numerals.
Rapid Recall
Solved Examples
Example 1: Find the numerical value of the following expressions:
a. IX + I
b. IX + V – I
c. IX + L
d. XI + IX
e. XI – IX
Solution:
a. IX + I
IX → 9
I → 1
So, IX + I → 9 + 1
= 10
Hence, IX + I is equal to 10.
b. IX + V – I
IX → 9
V → 5
I → 1
So, IX + V – I → 9 + 5 – 1
= 13
Hence, IX + V – I is equal to 13.
c. IX + L
IX → 9
L → 50
So, IX + L → 9 + 50
= 59
Hence, IX + L is equal to 59.
d. XI + IX
IX → 9
XI → 11
So, IX + XI → 9 + 11
= 20
Hence, IX + XI is equal to 20.
e. XI – IX
XI → 11
IX → 9
So, IX – XI → 11 – 9
= 2
Hence, XI – IX is equal to 2.
The additive form notation for the number 5 in Roman numerals is IIIII.
Roman numerals in the current era can be seen used by monarchs and Popes with their name and titles, as chapter numbers in books and in clocks.
The Roman numeral for 100 is C.