Roman Numerals (I to XX)
Roman numerals are a number system that originated in ancient Rome. They use letters of the alphabet to represent numbers. In Class 3, students learn Roman numerals from I to XX (1 to 20).
Roman numerals are still used today on clock faces, in book chapters, and for numbering lists.
What is Roman Numerals (I to XX) - Class 3 Maths (Numbers up to 1000)?
Roman numerals use seven basic symbols. For numbers 1 to 20, we use three of them:
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
Rules for writing Roman numerals:
- Repetition: A symbol can be repeated up to 3 times to add its value. II = 2, III = 3, XX = 20.
- Addition: When a smaller value comes after a larger value, add them. VI = 5 + 1 = 6.
- Subtraction: When a smaller value comes before a larger value, subtract. IV = 5 − 1 = 4.
- V and X are never repeated.
| Number | Roman | Number | Roman |
|---|---|---|---|
| 1 | I | 11 | XI |
| 2 | II | 12 | XII |
| 3 | III | 13 | XIII |
| 4 | IV | 14 | XIV |
| 5 | V | 15 | XV |
| 6 | VI | 16 | XVI |
| 7 | VII | 17 | XVII |
| 8 | VIII | 18 | XVIII |
| 9 | IX | 19 | XIX |
| 10 | X | 20 | XX |
Solved Examples
Example 1: Writing a Number in Roman Numerals
Question: Write 7 in Roman numerals.
Think:
- 7 = 5 + 2
- 5 = V, 2 = II
- Write V first, then II after it
Answer: 7 = VII
Example 2: Roman Numeral with Subtraction Rule
Question: Write 9 in Roman numerals.
Think:
- 9 = 10 − 1
- Place I (1) before X (10) to show subtraction
Answer: 9 = IX
Example 3: Converting Roman to Hindu-Arabic
Question: What number does XIV represent?
Think:
- X = 10
- I before V means subtraction: IV = 4
- 10 + 4 = 14
Answer: XIV = 14
Example 4: Converting Roman to Hindu-Arabic (Addition)
Question: What number does XVII represent?
Think:
- X = 10, V = 5, II = 2
- All values decrease from left to right → add them
- 10 + 5 + 1 + 1 = 17
Answer: XVII = 17
Example 5: Word Problem — Clock Face
Question: Ria looks at a clock with Roman numerals. The hour hand points to XII. What time is the hour?
Think:
- XII = X + I + I = 10 + 1 + 1 = 12
Answer: The hour hand shows 12 o'clock.
Example 6: Comparing Roman Numerals
Question: Which is greater: VIII or VI?
Think:
- VIII = 8
- VI = 6
- 8 > 6
Answer: VIII (8) is greater than VI (6).
Example 7: Writing 4 in Roman Numerals
Question: Why is 4 written as IV and not IIII?
Think:
- A symbol can be repeated at most 3 times
- So we cannot write IIII
- Instead, write I before V: IV = 5 − 1 = 4
Answer: 4 = IV (using the subtraction rule, because I cannot be repeated 4 times).
Example 8: Word Problem — Book Chapters
Question: Aman is reading Chapter XVIII of his science book. Which chapter number is this?
Think:
- X = 10, V = 5, III = 3
- 10 + 5 + 3 = 18
Answer: Aman is reading Chapter 18.
Example 9: Adding Roman Numerals
Question: Find XII + III. Write the answer in Roman numerals.
Think:
- XII = 12, III = 3
- 12 + 3 = 15
- 15 in Roman numerals = XV
Answer: XII + III = XV
Example 10: Ordering Roman Numerals
Question: Arrange in ascending order: IX, IV, VII, II.
Think:
- IX = 9, IV = 4, VII = 7, II = 2
- Ascending order: 2, 4, 7, 9
Answer: II, IV, VII, IX
Real-World Applications
Where are Roman numerals used today?
- Clocks and watches: Many clock faces use Roman numerals I to XII for the hours.
- Books: Chapter numbers are often written in Roman numerals: Chapter I, Chapter II, Chapter III.
- Class names: In some schools, classes are written as Class I, Class II, Class III.
- Movie sequels: Films like 'Dhoom 2' could be written as 'Dhoom II'.
- Buildings: Year of construction on old buildings is written in Roman numerals (e.g., MCMXL = 1940).
- Outlines and lists: Roman numerals are used for main headings: I, II, III, IV.
- Olympics: The Olympic Games are numbered using Roman numerals.
While we use Hindu-Arabic numerals (1, 2, 3...) for calculations, Roman numerals are still used for labelling and decoration. Knowing how to read them is a useful skill.
Key Points to Remember
- Roman numerals use letters: I = 1, V = 5, X = 10.
- A symbol can be repeated up to 3 times (III = 3, but IIII is not allowed).
- Addition rule: Smaller value after larger value → add (VI = 6).
- Subtraction rule: Smaller value before larger value → subtract (IV = 4, IX = 9).
- V and X are never repeated.
- Roman numerals have no symbol for zero.
Practice Problems
- Write 13 in Roman numerals.
- What number does XIX represent?
- Write 11 in Roman numerals.
- Arrange in descending order: XV, VIII, XII, III.
- Is IIII a valid Roman numeral? Why or why not?
- Priya reads Chapter XVI. Which chapter number is it?
- Find IX + VI and write the answer in Roman numerals.
- What is the largest number you can write using I, V, and X (up to XX)?
Frequently Asked Questions
Q1. What are Roman numerals?
Roman numerals are a number system from ancient Rome that uses letters (I, V, X, L, C, D, M) to represent numbers. In Class 3, we learn I (1), V (5), and X (10) to write numbers from 1 to 20.
Q2. Why is 4 written as IV and not IIII?
The rule says a symbol can be repeated at most 3 times. Since IIII would repeat I four times, we use the subtraction rule: IV means 5 minus 1 = 4.
Q3. Is there a Roman numeral for 0?
No. The Roman numeral system has no symbol for zero. The concept of zero was not part of the original Roman system.
Q4. Where do we see Roman numerals today?
Roman numerals appear on clock faces, in book chapters, on building cornerstones (year of construction), in movie titles (sequel numbers), and in outlines or lists.
Q5. How do you know when to add and when to subtract?
If a smaller value appears before a larger value, subtract it (IV = 4). If a smaller value appears after a larger value, add it (VI = 6). Read from left to right.
Q6. Can V be repeated?
No. V (5) and X (10) are never repeated. To write 10, use X (not VV). To write 20, use XX.
Q7. How do you write 15 in Roman numerals?
15 = 10 + 5 = XV. Write X first (10), then V (5) after it.
Q8. What is the difference between Roman numerals and Hindu-Arabic numerals?
Hindu-Arabic numerals (1, 2, 3...) use place value and the digit 0. Roman numerals (I, II, III...) use letters and have no zero. Hindu-Arabic numerals are used for calculations; Roman numerals are used for labelling.
