Roman Numbers

At some point of time in our lives, we must have seen these type of numbers on antique clocks worldwide. It is now considered stylistic to have devices that shows the numbers in Roman number. Many of the readers may have seen the Roman numbers on the Nobel prize medals, Big ben, and all the big clocks placed near the townhalls or near the courts of cities across the world.

Roman numerals are written in a certain way because the system is fundamentally additive and subtractive, rather than place-valued like Hindu-Arabic numerals (0-9). Hence, zero is not seen as a separate symbol in the number system.

Here’s a breakdown of the “why” behind their design:

1. The Origin: A Tally System

At its heart, the Roman numeral system started as a simple tally system, much like a shepherd counting sheep by making marks on a stick.

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100 (From the Latin word centum, meaning hundred)
• D = 500
• M = 1000 (From the Latin word mille, meaning thousand)

2. The Reason for the Subtractive Principle (IV instead of IIII)

• Efficiency and Clarity
• Preventing Confusion
• Intellectual Elegance: Showing an understanding that 4 is “one before five”, or “one less than five.”

3. Why There is No Zero

This is a crucial point. The Roman system was designed for counting and recording quantities, not for doing mathematical calculations like multiplication or division.

• Practical Use: They were used for commerce, military records, dates on monuments, and numbering chapters. For these purposes, you don’t need a zero. You are counting things that exist.
• Philosophical Concept: The concept of “nothing” as a number was alien to their practical, engineering-focused mindset. A placeholder for “nothing” wasn’t necessary in their additive system.

4. Roman numbers from 1 to 100

Now, let us see and learn the numbers in the system from 1 to 100. You can see that from 11 to 100, there are patterns in symbols, groups of symbols that are used in either additive or subtractive manner. (E.g. if symbols of less value are placed on the left of symbols of greater value [I placed before V or X], then we have to subtract value of left symbol from the value of right symbols [subtract one from five]).

One to fifty in Roman and Decimal

I = One II = Two (1+1) III = Three (1+1+1) IV = Four (5-1) V = Five VI = Six (5+1) VII = Seven (5+2) VIII = Eight (5+3) IX = Nine (10-1) X = Ten

XI = Eleven XII = Twelve XIII = Thirteen XIV = Fourteen (10+4) XV = Fifteen XVI = Sixteen XVII = Seventeen XVIII = Eighteen XIX = Nineteen (10+9) XX = Twenty

XXI = Twenty-one XXII = Twenty-two XXIII = Twenty-three XXIV = Twenty-four XXV = Twenty-five XXVI = Twenty-six XXVII = Twenty-seven XXVIII = Twenty-eight XXIX = Twenty-nine XXX = Thirty

XXXI = Thirty-one XXXII = Thirty-two XXXIII = Thirty-three XXXIV = Thirty-four XXXV = Thirty-five XXXVI = Thirty-six XXXVII = Thirty-seven XXXVIII = Thirty-eight XXXIX = Thirty-nine XL = Forty (50-10)

XLI = Forty-one XLII = Forty-two XLIII = Forty-three XLIV = Forty-four XLV = Forty-five XLVI = Forty-six XLVII = Forty-seven XLVIII = Forty-eight XLIX = Forty-nine L = Fifty

Fifty-one to Hundred in Roman and Decimal

LI = Fifty-one LII = Fifty-two LIII = Fifty-three LIV = Fifty-four LV = Fifty-five LVI = Fifty-six LVII = Fifty-seven LVIII = Fifty-eight LIX = Fifty-nine LX = Sixty

LXI = Sixty-one LXII = Sixty-two LXIII = Sixty-three LXIV = Sixty-four LXV = Sixty-five LXVI = Sixty-six LXVII = Sixty-seven LXVIII = Sixty-eight LXIX = Sixty-nine LXX = Seventy

LXXI = Seventy-one LXXII = Seventy-two LXXIII = Seventy-three LXXIV = Seventy-four LXXV = Seventy-five LXXVI = Seventy-six LXXVII = Seventy-seven LXXVIII = Seventy-eight LXXIX = Seventy-nine LXXX = Eighty

LXXXI = Eighty-one LXXXII = Eighty-two LXXXIII = Eighty-three LXXXIV = Eighty-four LXXXV = Eighty-five LXXXVI = Eighty-six LXXXVII = Eighty-seven LXXXVIII = Eighty-eight LXXXIX = Eighty-nine XC = Ninety (100-10)

XCI = Ninety-one XCII = Ninety-two XCIII = Ninety-three XCIV = Ninety-four XCV = Ninety-five XCVI = Ninety-six XCVII = Ninety-seven XCVIII = Ninety-eight XCIX = Ninety-nine C = One hundred

5. Other important examples

Let’s say that we have to write the roman numbers for following years: 1998 and 2025.
1. We have to break down the number 1998.
1998 = 1000 + 900 + 90 + 8
And 900 = 1000 – 100 = CM
Therefore, 1998 = 1000 + 900 + 90 + 8
M = 1000; CM = 900; 90 = XC; 8 = VIII
1998 = MCMXCVIII

2. Let’s break down 2025:
2025 = 2000 + 20 + 5
2000 = MM; 20 = XX; 5 = V
Therefore, 2025 = MMXXV.

Conclusion

The system of numbers is obviously not in use today. But we can imagine that the system was invented back then to count up to a certain number of things. The key to practice these numbers is always break down all the big numbers into small numbers and use the basic symbols of Roman numerals (I,V,X,L,C,D,M) to form the Roman number against the decimal number given in the problem.

There are many number systems that are in existence but may be outdated. I will be discussing about them in upcoming articles. Doing this exercise can help you think and understand how people in earlier days of civilization solved the problems about counting and introducing a fair system to measure quantities of things for equal distribution of materials related to food and construction for infrastructure.

All the best learning this exercise; and enjoy this number system and its beauty.