Number & place value
Roman Numerals: I to M and Years
Year 3 · Year 4 · Year 5 · Year 6
- ✓By the end of this lesson students will be able to recognise and recall the value of Roman numerals I, V, X, L, C, D and M.
- ✓By the end of this lesson students will be able to convert Roman numerals up to M (1000) into standard (Arabic) numbers.
- ✓By the end of this lesson students will be able to convert standard (Arabic) numbers up to M (1000) into Roman numerals.
- ✓By the end of this lesson students will be able to read and write years using Roman numerals.
Key concepts
Roman numerals are a number system that originated in ancient Rome. Unlike our standard number system (called Arabic numerals), Roman numerals do not use place value and do not have a symbol for zero. They are still used today for things like clock faces, chapter numbers in books, and to show years on buildings or films.
There are seven basic symbols used in the Roman numeral system, each with a fixed value: I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000
To form larger numbers, Roman numerals follow a set of rules: 1. **Addition Rule**: When a numeral of equal or smaller value is placed after a numeral of greater value, their values are added together. For example, VI = 5 + 1 = 6, and LX = 50 + 10 = 60. 2. **Repetition Rule**: The numerals I, X, C, and M can be repeated up to three times to add their values. For example, III = 1 + 1 + 1 = 3, and XXX = 10 + 10 + 10 = 30. The numerals V, L, and D are never repeated. 3. **Subtraction Rule**: When a numeral of smaller value is placed immediately before a numeral of greater value, the smaller value is subtracted from the larger value. This rule only applies to specific pairs: * I can be placed before V (IV = 5 - 1 = 4) and X (IX = 10 - 1 = 9). * X can be placed before L (XL = 50 - 10 = 40) and C (XC = 100 - 10 = 90). * C can be placed before D (CD = 500 - 100 = 400) and M (CM = 1000 - 100 = 900). You cannot use more than one smaller numeral for subtraction (e.g., IIX is not 8, it should be VIII).
To write a year in Roman numerals, you usually break the number down into its thousands, hundreds, tens, and units, and then convert each part. For example, to write the year 1994: 1. Break it down: 1000 + 900 + 90 + 4 2. Convert each part: M + CM + XC + IV 3. Combine them: MCMXCIV
Key facts to remember
- 1The seven basic Roman numerals are I (1), V (5), X (10), L (50), C (100), D (500), M (1000).
- 2Roman numerals do not have a symbol for zero and do not use place value.
- 3When a smaller numeral is placed after a larger one, you add their values (e.g., VI = 6).
- 4When a smaller numeral is placed before a larger one, you subtract the smaller from the larger (e.g., IV = 4).
- 5The only subtraction pairs allowed are IV, IX, XL, XC, CD, CM.
- 6Numerals I, X, C, M can be repeated up to three times (e.g., XXX = 30).
- 7Numerals V, L, D are never repeated.
Worked examples
Example 1
Convert the Roman numeral LXI to a standard (Arabic) number.
Answer
61
This example uses the addition rule.
Example 2
Convert the Roman numeral MCMXCIV to a standard (Arabic) number.
Answer
1994
This example demonstrates both addition and subtraction rules, often used for years.
Example 3
Write the year 2023 in Roman numerals.
Answer
MMXXIII
Remember to convert each part of the number (thousands, hundreds, tens, units) separately before combining them.
Common mistakes
- ✗Repeating V, L, or D (e.g., VV for 10 is incorrect, it should be X).
- ✗Using incorrect subtraction pairs (e.g., IL for 49 is incorrect, it should be XLIX).
- ✗Using more than one smaller numeral for subtraction (e.g., IIX for 8 is incorrect, it should be VIII).
- ✗Not arranging numerals from largest to smallest value, unless using the subtraction rule (e.g., writing IXI instead of XCIX for 99).
- ✗Confusing C (100) and D (500), or L (50) and X (10).
Exam tips
- ★Memorise the seven basic Roman numerals and their values (I, V, X, L, C, D, M).
- ★When converting from Roman to Arabic, always look for subtraction pairs first (IV, IX, XL, XC, CD, CM) before adding.
- ★When converting from Arabic to Roman, break the number down into thousands, hundreds, tens, and units, then convert each part separately.
- ★Practise writing common years (e.g., your birth year, the current year) in Roman numerals to become more familiar with the system.
Ready to practise?
Try a problem on this topic
Snap a photo or type a question — get step-by-step working instantly.