Basic 5 · Mathematics · Counting, Representation and Cardinality
Roman Numerals up to 100
In this topic you will count and convert between Hindu-Arabic numbers and Roman numerals up to 100 (C).
By the end of these notes you should be able to:
- Recognise the Roman symbols I, V, X, L and C
- Apply the rules for forming Roman numerals
- Convert numbers up to 100 between the two systems
What you already know
- Roman numerals up to 30 (Basic 4)
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
- Strand
- Number
- Sub-strand
- Counting, Representation and Cardinality
- Indicator
- B5.1.1.2.1 – Count and convert Hindu-Arabic numbers to Roman numerals up to 100 (C) and vice versa
Introduction
Look at the names of kings such as Pope John Paul II or the chapters in some books: Chapter XL. To read these we need Roman numerals beyond 30.
1. The Symbols
| Roman | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
2. The Rules
- Add when a symbol is followed by an equal or smaller symbol: LX = 50 + 10 = 60.
- Subtract when a smaller symbol comes before a larger one: XL = 50 − 10 = 40; XC = 100 − 10 = 90.
- Only I, X and C can be placed before a larger symbol to subtract. I goes before V or X; X goes before L or C.
- A symbol may be repeated up to three times: XXX = 30. V and L are never repeated.
| Number | Roman | Number | Roman |
|---|---|---|---|
| 10 | X | 60 | LX |
| 20 | XX | 70 | LXX |
| 30 | XXX | 80 | LXXX |
| 40 | XL | 90 | XC |
| 50 | L | 100 | C |
3. Converting
Example 1
Write 74 in Roman numerals.
- 74 = 70 + 4
- 70 = LXX
- 4 = IV
Answer: LXXIV
Example 2
Write 99 in Roman numerals.
- 99 = 90 + 9
- 90 = XC
- 9 = IX
Answer: XCIX
Example 3
Write XLVIII as a number.
- XL = 40
- VIII = 8
Answer: 48
Common mistake: 99 is not IC. Write tens and ones separately: XC + IX = XCIX.
4. Where Roman Numerals Are Used Today
Roman numerals are still used on some clock faces, in the names of kings and queens (Queen Elizabeth II), for chapter and volume numbers in books, and for big events. To read a Roman numeral, break it into parts from left to right: tens first, then ones. For example, LXXVI = L + XX + VI = 50 + 20 + 6 = 76. The Romans had no symbol for zero, so there is no Roman numeral for 0.
New words
- Roman numerals
- Number symbols used by the ancient Romans.
- Hindu-Arabic numerals
- The digits 0–9 used every day.
- convert
- To change from one form to another.
- L
- The Roman numeral for 50.
- C
- The Roman numeral for 100.
- subtractive form
- Writing a smaller symbol before a larger one to subtract.
Summary
- I = 1, V = 5, X = 10, L = 50, C = 100.
- Add when an equal or smaller symbol follows; subtract when a smaller one comes first.
- Only I, X and C are used to subtract.
- Convert tens and ones separately, e.g. 99 = XC + IX.
Class activity: Roman Relay
- Write numbers from 1 to 100 on cards.
- Each member converts a card to Roman numerals and passes it on.
- The group checks every answer with the rules.
You need: Bundles of sticks, Locally made Roman numeral cards, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. What is L?
- A. 50
- B. 5
- C. 100
- D. 10
Show answer
Answer: 50L = 50.2. How is 40 written?
- A. XL
- B. XXXX
- C. LX
- D. VL
Show answer
Answer: XL50 − 10 = 40.3. What is XCV?
- A. 95
- B. 85
- C. 105
- D. 115
Show answer
Answer: 9590 + 5 = 95.4. C stands for 100.
- A. True
- B. False
Show answer
Answer: TrueC = 100.5. 49 is written as IL.
- A. True
- B. False
Show answer
Answer: False49 = XL + IX = XLIX.6. 60 in Roman numerals is ______.
Show answer
Answer: LX50 + 10.7. Write 83 and 67 in Roman numerals.
Show answer
Answer: LXXXIII and LXVII80 + 3 and 60 + 7.8. Write LXXXIX as a number and explain.
Show answer
Answer: 89: LXXX = 80 and IX = 9.Split into tens and ones.
Homework
- Write the ages of five family members in Roman numerals.