CAT 2025 Lesson : Number Systems - Roman Numerals

So far, we have worked with the Base $10$ number system. In this lesson, we will learn about other number systems.

1. Roman Numerals

This numeric system originated in ancient Rome over $2000$ years ago. Instead of using separate symbols (like in our decimal system) to represent numbers, they utilised the following letters of the Latin alphabet to represent these values.

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

Numbers were expressed by writing these symbols together. The following algorithm/rules are applied to compute the value of the number.

1) The value of a symbol is subtracted, if it is written to the left of a higher-valued symbol.
2) If not, the value of the symbol is added.

For example,
VIII $= 5 + 1 + 1 + 1 = 8$
IX $= -1 + 10 = 9$
XLIV $= -10 + 50 -1 + 5 = 44$
CDLVII $= -100 + 500 + 50 + 5 + 1 + 1 = 457$

Note that $49$ is written as XLIX and not IL. This is because of the following additional rules.

1) I can be written before V or X only
2) X can be written before L or C only.
3) C can be written before D or M only.

In Roman Numerals, $0$ or negative numbers cannot be written and decimals cannot be represented. Large numbers are difficult to write. For instance, the distance between sun and the earth is written as $150,000,000$ km in the decimal system. To write this in Roman Numerals, the symbol M has to be written $150,000$ times.

Upon the advent of the decimal system, Roman Numerals for mathematical operations ceased. Today we use Roman Numerals to indicate smaller numbers, such as the hours in a clock, the class in school, movie sequel numbers, book volumes, etc.