Roman Numerals – Definition with Examples

What Are Roman Numerals?

Roman numerals are a numbering system used to denote a fixed integer value. Roman numerals are symbols representing numbers that do not follow the base 10 number system.

Initially, fingers were used for counting. However, the ancient Romans discovered that counting on one’s fingers gets complicated as a number approaches ten. As a result, a standardized system for commerce and communication was required, and that resulted in the Roman Numeral system.

Roman Symbols

There are seven Roman symbols that are used to write thousands of different numbers. These symbols are Latin letters representing a specific value. 

roman symbols to write numbers

All other Roman numerals can be made using these seven Roman symbols.

We can simply represent 100 using C or 1000 using M. 

Similarly, to write 200 in Roman numerals, we just add the letters “C + C”. So CC represents 200 in Roman numbers. And to write 2050 in Roman numerals, we will add the letters “M+M+L”. So MML will be the representation of 2050 in Roman numbers.

Rules for Writing Roman Numerals

  • If a lower value digit is written to the right of a higher value digit, it is added.

For example: XV

Since V is lower value digit and is placed to the right of X, they will be added.

XV = X + V = 10 + 5 = 15

Hence, XV represents the number 15.

  • If a lower value digit is written to the left of a higher value digit, it is subtracted.

In this case, we can’t write any two Roman numerals together. The only allowed cases are: IV, IX, XL, XC, CD, CM. To calculate the value, subtract the first symbol from the second.

For example, for XL

We will subtract X, i.e., 10 from L, i.e., 50. 

50 – 10 = 40 

Hence, the Roman numeral XL represents 40.

  • The Roman numerals I, X, C cannot be repeated more than three times in succession.

So we do not write numbers 4 as IIII. The roman numeral ‘IV’ is used to represent the number four. We have I (1) before V (5). Because the smaller number comes before the larger, we know we must subtract to get IV (4). 

The number nine, written as IX, follows the same pattern.

Converting Numbers to Roman Numerals

We can convert a natural number to a Roman numeral by modifying the placement of the seven Roman letters/symbols. 

Follow the steps below:

Step 1: Split the number to be converted into the least expandable form.

Step 2: Write their respective Roman letters.

Step 3: Add or subtract them.

For example, to write 2052 as a Roman numeral:

Step 1: 1000 + 1000 + 50 + 1 + 1

Step 2: M + M + L + I + I

Step 3: MMLII

So, 2052 in Roman numerals = MMLII

Converting Roman Numerals to Numbers

Similarly, we can convert Roman numerals to numbers by following these steps:

Step 1: Split the Roman numerals into single letters.

Step2: Write their numerical value.

Step3: Add or subtract them.

For example, to convert XVII to a number:

Step 1: X + V + I + I

Step 2: 10 + 5 + 1 + 1

Step 3: 17

So, the Roman numeral XVII represents number 17.

Real-Life Applications of Roman Numerals

Here are some real-life applications of Roman numerals:

Real-Life examples of Roman Numerals

We have now learned about Roman numerals and their history in this article. We learned the different principles for writing Roman numerals and how to build numbers using them. SplashLearn’s math games for children make learning math more fun!

Solved Examples

There are fixed symbols for some Roman numerals, but how to write other numbers? Let us see with the help of some solved examples.

If you write a lower value symbol to the left of the greater value symbol, its value can be subtracted from the value of the greater symbol.

IV = 5 – 1 = 4

XL = 50 – 10=40

IX = 10 – 1 = 9

Similarly, if the symbol of greater value is written to the left of the lower value symbol, then their values can be added:

VI = 5 + 1 = 6

VII = 5 + 2 = 7

LXX = 50 + 10 + 10 = 70

Practice Problems

Roman Numerals

Attend this Quiz & Test your knowledge.

1How many basic numerals are there in the Roman numeration system?

10
7
8
11
CorrectIncorrect
Correct answer is: 7
There are seven roman symbols that are used to write thousands of different numbers. All other Roman Numerals can be made using these 7 Roman Symbols.

2Which basic Roman Numeral can not be subtracted?

V
X
II
III
CorrectIncorrect
Correct answer is: V
The symbol V is not written to the left of a symbol that has greater value. This means that V is never subtracted.

3What is the equivalent number for the numeral ‘X’?

10
7
9
2
CorrectIncorrect
Correct answer is: 10
Number 10 is represented by X in roman numeral.

Frequently Asked Questions

V is the Roman numeral for 5 and (V) stands for Roman numeral 5000. These numerals can also be written with an overline or between two vertical lines to indicate multiplication by 1000.
It is preferred to write them between brackets.

The letters V, L, and D are never used more than once. Likewise, a symbol is never used more than three times in a row. 

There is no symbol for “0” in Roman numerals. It is because they started counting from one; the Romans did not require a zero in their additive system.

Around 500 B.C.E, the Romans devised a numeral system for representing numbers. As the Romans conquered much of the known world, their numeral system expanded throughout Europe, where Roman numerals remained the primary method of number representation for centuries.