Roman Numerals — 1 to 1000

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Introduction — The Story of Roman Numerals

Thousands of years ago, the ancient Romans needed a way to count and record numbers. They did not use the digits 0, 1, 2, 3... like we do today. Instead, they created a system using letters of the alphabet to represent numbers. This system is called the Roman Numeral System.

Even though we now use the Hindu-Arabic numeral system (0–9) for most calculations, Roman numerals are still used in many places around the world — and in India too!

Where Do We See Roman Numerals Today?

Think About It: Next time you visit a historical monument like India Gate, Rashtrapati Bhavan, or Victoria Memorial in Kolkata, look for Roman numerals carved in the stone. They usually show the year the building was constructed!

The 7 Basic Symbols of Roman Numerals

The entire Roman numeral system uses only 7 symbols. Every Roman numeral from 1 to 1000 (and beyond) is written using combinations of these seven letters:

Roman SymbolHindu-Arabic ValueName
I1One
V5Five
X10Ten
L50Fifty
C100One Hundred
D500Five Hundred
M1000One Thousand
Image needed: A colourful chart showing all 7 Roman numeral symbols (I, V, X, L, C, D, M) with their values. Each symbol in a large bold font inside a coloured circle or badge with the Hindu-Arabic value below. Arranged in ascending order left to right.
Style: Clean flat illustration, bright colours, child-friendly, large bold letters
Size: 800×300px

Easy Memory Trick

Remember the symbols in order using this sentence:

I Value Xtra Large Cakes Daily, Mummy!

(I=1, V=5, X=10, L=50, C=100, D=500, M=1000)

Did You Know? There is no symbol for zero in Roman numerals! The Romans did not have a concept of zero. This is one reason why the Hindu-Arabic system (which has zero) is better for calculations.

Rules of the Roman Numeral System

Roman numerals follow strict rules. You must understand these rules to read and write Roman numerals correctly.

Rule 1: Repetition (Adding by Repeating)

Rule 1

  • A symbol can be repeated to add its value. Each repetition adds the value once more.
  • A symbol can be repeated a maximum of 3 times in a row.
  • Only I, X, C, and M can be repeated.
  • V, L, and D are NEVER repeated.
Examples:
II = 1 + 1 = 2
III = 1 + 1 + 1 = 3
XX = 10 + 10 = 20
XXX = 10 + 10 + 10 = 30
CC = 100 + 100 = 200
CCC = 100 + 100 + 100 = 300
MM = 1000 + 1000 = 2000 (but this is beyond 1000)

Wrong: IIII (cannot repeat more than 3 times — use IV instead)
Wrong: VV (V cannot be repeated — use X instead)
Wrong: LL (L cannot be repeated — use C instead)

Rule 2: Addition (Smaller After Larger = Add)

Rule 2

  • When a smaller value symbol is placed after (to the right of) a larger value symbol, we add the values.
Examples:
VI = 5 + 1 = 6
VII = 5 + 1 + 1 = 7
VIII = 5 + 1 + 1 + 1 = 8
XI = 10 + 1 = 11
XV = 10 + 5 = 15
LX = 50 + 10 = 60
CX = 100 + 10 = 110
DC = 500 + 100 = 600
MC = 1000 + 100 = 1100 (beyond our range, but valid)

Rule 3: Subtraction (Smaller Before Larger = Subtract)

Rule 3

  • When a smaller value symbol is placed before (to the left of) a larger value symbol, we subtract the smaller from the larger.
  • This is used to avoid writing a symbol 4 times.
The 6 Subtraction Combinations:
IV = 5 − 1 = 4
IX = 10 − 1 = 9
XL = 50 − 10 = 40
XC = 100 − 10 = 90
CD = 500 − 100 = 400
CM = 1000 − 100 = 900

Rule 4: Only I, X, and C Can Be Subtracted

Rule 4

  • V, L, and D are NEVER used for subtraction.
  • Only I, X, and C can be placed before a larger symbol to subtract.
Wrong: VX (cannot subtract V from X — write 5 as V)
Wrong: LC (cannot subtract L from C — write 50 as L)
Wrong: DM (cannot subtract D from M — write 500 as D)

Rule 5: Subtraction Limits

Rule 5

  • I can only be subtracted from V (to make 4) and X (to make 9).
  • X can only be subtracted from L (to make 40) and C (to make 90).
  • C can only be subtracted from D (to make 400) and M (to make 900).
Wrong: IC (trying to write 99 as I before C) — this is INVALID!
Correct: 99 = 90 + 9 = XC + IX = XCIX

Wrong: IM (trying to write 999 as I before M) — this is INVALID!
Correct: 999 = 900 + 90 + 9 = CM + XC + IX = CMXCIX

Wrong: XM (trying to write 990 as X before M) — this is INVALID!
Correct: 990 = 900 + 90 = CM + XC = CMXC

Rule 6: Reading Complex Numerals

Rule 6

  • When a smaller numeral appears between two larger numerals, it is subtracted from the one that follows it (the one on its right).
  • Read Roman numerals from left to right, applying subtraction only where a smaller symbol directly precedes a larger one.
Examples:
XIV = X + IV = 10 + (5−1) = 10 + 4 = 14
XIX = X + IX = 10 + (10−1) = 10 + 9 = 19
XLIV = XL + IV = (50−10) + (5−1) = 40 + 4 = 44
XCIX = XC + IX = (100−10) + (10−1) = 90 + 9 = 99
CDXLIX = CD + XL + IX = 400 + 40 + 9 = 449
Image needed: A visual diagram showing all 6 rules of Roman numerals. Use arrows and colour coding — green arrows for addition (smaller after larger), red arrows for subtraction (smaller before larger). Show examples: VI (add), IV (subtract), XXX (repeat). Include a "NEVER repeat" warning for V, L, D.
Style: Educational diagram, colour-coded, child-friendly, labelled clearly
Size: 800×500px

Roman Numerals — 1 to 20

Here is the complete table of Roman numerals from 1 to 20. Notice how the rules of addition and subtraction are applied:

NumberRomanHow It WorksNumberRomanHow It Works
1IOne unit11XI10 + 1
2II1 + 112XII10 + 1 + 1
3III1 + 1 + 113XIII10 + 1 + 1 + 1
4IV5 − 1 (subtraction)14XIV10 + (5−1)
5VBasic symbol15XV10 + 5
6VI5 + 116XVI10 + 5 + 1
7VII5 + 1 + 117XVII10 + 5 + 1 + 1
8VIII5 + 1 + 1 + 118XVIII10 + 5 + 1 + 1 + 1
9IX10 − 1 (subtraction)19XIX10 + (10−1)
10XBasic symbol20XX10 + 10
Pattern Alert: Notice that 4 and 9 use subtraction (IV, IX). Similarly, 14 and 19 also use subtraction (XIV, XIX). This pattern repeats at every level — 40 (XL), 90 (XC), 400 (CD), 900 (CM). Watch for it!

Roman Numerals — Tens (10 to 100)

The same addition and subtraction rules apply to tens. Here X plays the same role as I, and L and C play the roles of V and X at a higher level:

NumberRoman NumeralHow It Works
10XBasic symbol
20XX10 + 10 (repetition)
30XXX10 + 10 + 10 (repetition)
40XL50 − 10 (subtraction)
50LBasic symbol
60LX50 + 10 (addition)
70LXX50 + 10 + 10 (addition)
80LXXX50 + 10 + 10 + 10 (addition)
90XC100 − 10 (subtraction)
100CBasic symbol

Roman Numerals — Hundreds (100 to 1000)

At the hundreds level, C plays the same role as I and X. D and M play the roles of V and X at this higher level:

NumberRoman NumeralHow It Works
100CBasic symbol
200CC100 + 100 (repetition)
300CCC100 + 100 + 100 (repetition)
400CD500 − 100 (subtraction)
500DBasic symbol
600DC500 + 100 (addition)
700DCC500 + 100 + 100 (addition)
800DCCC500 + 100 + 100 + 100 (addition)
900CM1000 − 100 (subtraction)
1000MBasic symbol

The Pattern at Every Level

Notice how the pattern is identical at ones, tens, and hundreds:

Value123456789
OnesIIIIIIIVVVIVIIVIIIIX
TensXXXXXXXLLLXLXXLXXXXC
HundredsCCCCCCCDDDCDCCDCCCCM

How to Convert Hindu-Arabic Numbers to Roman Numerals

To convert a number (like 849) to Roman numerals, follow this step-by-step method:

Step-by-Step Method

  • Step 1: Break the number into its place values (hundreds, tens, ones).
  • Step 2: Convert each part to Roman numerals separately.
  • Step 3: Write them together from left to right (largest to smallest).
Example 1: Convert 276 to Roman numerals.
Step 1: 276 = 200 + 70 + 6
Step 2: 200 = CC, 70 = LXX, 6 = VI
Step 3: CCLXXVI
Example 2: Convert 849 to Roman numerals.
Step 1: 849 = 800 + 40 + 9
Step 2: 800 = DCCC, 40 = XL, 9 = IX
Step 3: DCCCXLIX
Example 3: Convert 999 to Roman numerals.
Step 1: 999 = 900 + 90 + 9
Step 2: 900 = CM, 90 = XC, 9 = IX
Step 3: CMXCIX
Example 4: Convert 1000 to Roman numerals.
1000 = M. That is it! The simplest one.
Answer: M
Example 5: Convert 467 to Roman numerals.
Step 1: 467 = 400 + 60 + 7
Step 2: 400 = CD, 60 = LX, 7 = VII
Step 3: CDLXVII
Example 6: Convert 594 to Roman numerals.
Step 1: 594 = 500 + 90 + 4
Step 2: 500 = D, 90 = XC, 4 = IV
Step 3: DXCIV

How to Convert Roman Numerals to Hindu-Arabic Numbers

To convert a Roman numeral (like CDLXVIII) to a regular number, follow these steps:

Step-by-Step Method

  • Step 1: Write the value of each symbol below it.
  • Step 2: Compare each symbol with the one to its right.
  • Step 3: If a symbol is smaller than the one to its right → subtract it.
  • Step 4: If a symbol is equal to or larger than the one to its right → add it.
  • Step 5: Calculate the total.
Example 1: Convert CDLXVIII to Hindu-Arabic.
C=100, D=500, L=50, X=10, V=5, I=1, I=1, I=1
C < D → subtract C: −100 + 500 = 400
L, X, V, I, I, I → all add: 50 + 10 + 5 + 1 + 1 + 1 = 68
Total: 400 + 68 = 468
Example 2: Convert CMXCIX to Hindu-Arabic.
C=100, M=1000, X=10, C=100, I=1, X=10
C < M → subtract: −100 + 1000 = 900
X < C → subtract: −10 + 100 = 90
I < X → subtract: −1 + 10 = 9
Total: 900 + 90 + 9 = 999
Example 3: Convert DCCXXXIV to Hindu-Arabic.
D=500, C=100, C=100, X=10, X=10, X=10, I=1, V=5
D, C, C, X, X, X → all add (each is ≥ the one to its right): 500 + 100 + 100 + 10 + 10 + 10 = 730
I < V → subtract: −1 + 5 = 4
Total: 730 + 4 = 734
Example 4: Convert MCMLXIV to Hindu-Arabic.
M=1000, C=100, M=1000, L=50, X=10, I=1, V=5
M → add: 1000
C < M → subtract: −100 + 1000 = 900
L → add: 50
X → add: 10
I < V → subtract: −1 + 5 = 4
Total: 1000 + 900 + 50 + 10 + 4 = 1964 (beyond 1000 but shows the method!)

Common Mistakes to Avoid

Students often make these errors when writing Roman numerals. Learn them so you never make them!

MistakeWhy It Is WrongCorrect Way
IIII for 4I cannot be repeated more than 3 timesIV (5 − 1 = 4)
VV for 10V can NEVER be repeatedX
LL for 100L can NEVER be repeatedC
DD for 1000D can NEVER be repeatedM
IC for 99I can only be subtracted from V and X (not C)XCIX (90 + 9)
IM for 999I can only be subtracted from V and X (not M)CMXCIX (900 + 90 + 9)
XM for 990X can only be subtracted from L and C (not M)CMXC (900 + 90)
VX for 5V cannot be used for subtractionV
IL for 49I can only be subtracted from V and X (not L)XLIX (40 + 9)
XXXX for 40X cannot be repeated more than 3 timesXL (50 − 10)
Memory Tip: The subtraction rule ONLY works in these pairs: I with V and X, X with L and C, C with D and M. A symbol can only be subtracted from the next two symbols above it in the table — never from anything higher.

Roman Numerals in Real Life — Indian Context

Roman numerals appear in many places around India and the world. Here are some fascinating examples:

On Monuments and Buildings

On Clocks and Watches

In Books, Movies, and Sports

Historical Years in Roman Numerals

EventYearRoman Numeral
India Gate completed1931MCMXXXI
Indian Independence1947MCMXLVII
Indian Republic Day1950MCML
Chandrayaan-3 landing2023MMXXIII
Current year2025MMXXV
Image needed: A collage showing Roman numerals in real life — a clock face with Roman numerals, India Gate with MCMXXXI visible, a book showing "Chapter IV", and an Olympic rings logo with XXXIII. All labelled clearly with arrows pointing to the Roman numerals.
Style: Photo-realistic collage style, labelled, child-friendly layout
Size: 800×450px

Key Words

TermMeaning
Roman NumeralA number system using 7 letters (I, V, X, L, C, D, M) invented by ancient Romans
Hindu-Arabic NumeralThe number system we use daily (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
RepetitionWriting a symbol more than once to increase its value (max 3 times)
Addition RuleWhen a smaller symbol follows a larger one, add them (VI = 5+1 = 6)
Subtraction RuleWhen a smaller symbol comes before a larger one, subtract it (IV = 5−1 = 4)
Place ValueThe value of a digit based on its position (units, tens, hundreds)
ConvertTo change from one form to another (e.g., 49 → XLIX)

Key Points to Remember

  • There are only 7 symbols in Roman numerals: I(1), V(5), X(10), L(50), C(100), D(500), M(1000).
  • I, X, C, M can be repeated up to 3 times. V, L, D are NEVER repeated.
  • Smaller after larger = ADD (VI = 6). Smaller before larger = SUBTRACT (IV = 4).
  • Only I, X, C can be used for subtraction. V, L, D are never subtracted.
  • I subtracts from V and X only. X subtracts from L and C only. C subtracts from D and M only.
  • There is no zero in the Roman numeral system.
  • To convert: break the number into hundreds + tens + ones, convert each part, then combine.
  • The 6 subtraction pairs are: IV(4), IX(9), XL(40), XC(90), CD(400), CM(900).
  • The largest number we can write using standard rules up to M is MMMCMXCIX = 3999.

Finished learning? Now test what you know!