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CAT 2025 Lesson : Number Systems - Roman Numerals
So far, we have worked with the Base number system. In this lesson, we will learn about other number systems.
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
IX
XLIV
CDLVII
Note that 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, 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 km in the decimal system. To write this in Roman Numerals, the symbol M has to be written 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.
1. Roman Numerals
This numeric system originated in ancient Rome over 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 | |
| V | |
| X | |
| L | |
| C | |
| D | |
| M |
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
IX
XLIV
CDLVII
Note that 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, 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 km in the decimal system. To write this in Roman Numerals, the symbol M has to be written 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.
Example 1
Which of the following equals the sum of the roman numbers CDLVI and CCXXXIX?
() CDXCVI () DCCXV () DCXCV () DCCXXI
CCXXXIX
We do not consider options and as their last digits are and respectively.
Option 2: DCCXV
Option 3: DCXCV
Answer: (3) DCXCV
() CDXCVI () DCCXV () DCXCV () DCCXXI
Solution
CDLVICCXXXIX
We do not consider options and as their last digits are and respectively.
Option 2: DCCXV
Option 3: DCXCV
Answer: (3) DCXCV
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