ROMAN NUMERALS

Roman numerals are an ancient system of writing numbers using special letters from the Latin alphabet. Instead of using digits like 0, 1, 2, or 3, this system uses letters to show values.

Example

The number 3 is written as III in Roman numerals because the letter I represents the number 1. When we repeat the letter three times, we add them together: 1 + 1 + 1 = 3.

The number 5 is written as a single letter V.

3 = III and 5 = V

We still use Roman numerals in everyday life for specific things:

Roman numerals are used in everyday life when:

Showing hours on clock faces and watches.
Writing chapter numbers or section headings in books.
Naming major sporting events, like the Olympic Games or the Super Bowl.
Showing the year a movie or building was made (found at the end of movie credits or on old walls).
Writing titles for kings and queens, like King George VI or Queen Elizabeth II.
Creating numbered lists in school assignments or documents.

Basic Roman Numeral Symbols

The Roman numeral system uses exactly seven basic letters as symbols. Every number is built by combining these seven symbols in different ways.

I: Represents the value 1
V: Represents the value 5
X: Represents the value 10
L: Represents the value 50
C: Represents the value 100
D: Represents the value 500
M: Represents the value 1,000

Roman Numeral Reference Chart (1 to 1000)

The table below shows how the basic symbols are combined to form landmark numbers from 1 all the way up to 1,000.

Number Range	Landmark Values and Symbols
1 to 10	1=I, 2=II, 3=III, 4=IV, 5=V, 6=VI, 7=VII, 8=VIII, 9=IX, 10=X
20 to 100 (Tens)	20=XX, 30=XXX, 40=XL, 50=L, 60=LX, 70=LXX, 80=LXXX, 90=XC, 100=C
200 to 1000 (Hundreds)	200=CC, 300=CCC, 400=CD, 500=D, 600=DC, 700=DCC, 800=DCCC, 900=CM, 1000=M

Rules for Writing Roman Numerals

To write numbers correctly with Roman numerals, you must follow four simple rules. These rules show you when to repeat, add, or subtract values.

1. Rule of Repetition

You can repeat the symbols I, X, C, and M up to three times in a row to add their values.

Important exception: The symbols V, L, and D can never be repeated. You can only write them once in a number.

Examples

Write 30 in Roman numerals.

solution: Repeat X three times: X + X + X = 10 + 10 + 10 = 30.

Result = XXX

Can you write 55 as VV?

solution: No. V cannot be repeated. The number 50 already has its own symbol, which is L. So, 55 must be written as LV.

Result = LV

2. Rule of Addition

When a smaller symbol is placed after a larger symbol, you must add the values together.

Examples

Find the value of VI.

solution: V (5) is larger than I (1). Since I comes after V, add them: 5 + 1 = 6.

Result = 6

Find the value of CLX.

solution: C is 100, L is 50, and X is 10. They are arranged from largest to smallest. Add them all up: 100 + 50 + 10 = 160.

Result = 160

3. Rule of Subtraction

When a smaller symbol is placed before a larger symbol, you must subtract the smaller value from the larger value.

Examples

Find the value of IV.

solution: I (1) comes before V (5). Subtract 1 from 5: 5 − 1 = 4.

Result = 4

Find the value of XC.

solution: X (10) comes before C (100). Subtract 10 from 100: 100 − 10 = 90.

Result = 90

4. Invalid Combinations and Subtraction Restrictions

You cannot subtract just any number from another. There are strict laws for subtraction:

I can only be subtracted from V and X (to make 4 and 9).
X can only be subtracted from L and C (to make 40 and 90).
C can only be subtracted from D and M (to make 400 and 900).
The symbols V, L, and D can never be subtracted from any larger number.

Examples

Can you write 95 as VC (100 − 5)?

solution: No. V can never be used for subtraction. To write 95, you must first write 90 (XC) and then add 5 (V).

Result = XCV

Can you write 99 as IC (100 − 1)?

solution: No. I can only be subtracted from V and X. To write 99, you must break it down into 90 (XC) and 9 (IX).

Result = XCIX

Conversions and Operations

To work with Roman numerals easily, you need to know how to change them back and forth with our regular numbers (Hindu-Arabic numerals). You can also add and subtract numbers directly using Roman numerals.

1. Converting Regular Numbers to Roman Numerals

To convert a regular number, expand it into thousands, hundreds, tens, and ones first. Then, convert each part into Roman symbols and join them together.

Example

Convert 443 into Roman numerals.

solution:

Step 1: Break the number down by its place values.

443 = 400 + 40 + 3

Step 2: Convert each value into its correct Roman symbols using the subtraction and addition rules.

400 is written as CD (500 − 100)
40 is written as XL (50 − 10)
3 is written as III (1 + 1 + 1)

Step 3: Join all the parts together in order from left to right.

CD + XL + III = CDXLIII

Final Answer = CDXLIII

2. Converting Roman Numerals to Regular Numbers

To change a Roman numeral back into a regular number, read the symbols from left to right. Check if a smaller symbol comes before a larger one to apply subtraction. Otherwise, add the values.

Example

Convert the Roman numeral MMCXXIV into a regular number.

solution:

Step 1: Read the grouped values from left to right.

MM: Two thousands combined = 1,000 + 1,000 = 2,000
C: One hundred = 100
XX: Two tens combined = 10 + 10 = 20
IV: A smaller value (I) is before a larger value (V). Subtract: 5 − 1 = 4

Step 2: Add all the calculated groups together.

Total = 2,000 + 100 + 20 + 4 = 2,124

Final Answer = 2,124

3. Addition and Subtraction Using Roman Numerals

When solving math equations written in Roman numerals, the easiest method is to convert the numerals into regular numbers, calculate the answer normally, and change the final result back into Roman numerals.

Example

Calculate: CLXV + XCIV and give your answer as a Roman numeral.

solution:

Step 1: Convert both Roman numerals into regular numbers.

CLXV = 100 + 50 + 10 + 5 = 165
XCIV = (100 − 10) + (5 − 1) = 90 + 4 = 94

Step 2: Add the regular numbers together.

165 + 94 = 259

Step 3: Convert the sum (259) back into Roman numerals.

200 = CC
50 = L
9 = IX

Join the symbols together: CC + L + IX = CCLIX

Final Answer = CCLIX

Worked Examples

Example 1

Convert the regular number 894 into Roman numerals.

solution :

Step 1: Expand the number by its individual place values.

894 = 800 + 90 + 4

Step 2: Convert each place value group into its matching Roman symbols.

800 is written as DCCC (500 + 100 + 100 + 100)
90 is written as XC (100 − 10 because a smaller value is placed before a larger one)
4 is written as IV (5 − 1 because a smaller value is placed before a larger one)

Step 3: Join all the sets of symbols together in order from left to right.

DCCC + XC + IV = DCCCXCIV

Final Answer = DCCCXCIV

Example 2

Convert the Roman numeral string CMLXXIX into a regular number.

solution :

Step 1: Scan and group the symbols from left to right, looking out for subtraction pairs.

CM: The smaller symbol C (100) is before the larger M (1,000). Subtract: 1,000 − 100 = 900.
LXX: The symbols decrease in size normally. Add: 50 + 10 + 10 = 70.
IX: The smaller symbol I (1) is before the larger X (10). Subtract: 10 − 1 = 9.

Step 2: Add all the grouped values together to calculate the complete total.

Total = 900 + 70 + 9 = 979

Final Answer = 979

Example 3

Evaluate the expression: CDXXXVI − CCLXIV. Give your final result using Roman numerals.

solution :

Step 1: Convert the first Roman numeral string into a regular number.

CDXXXVI = CD (400) + XXX (30) + VI (6) = 436

Step 2: Convert the second Roman numeral string into a regular number.

CCLXIV = CC (200) + LX (60) + IV (4) = 264

Step 3: Perform the subtraction operation using the regular values.

436 − 264 = 172

Step 4: Convert the numerical answer 172 back into Roman symbols.

172 = 100 + 70 + 2 = C + LXX + II = CLXXII

Final Answer = CLXXII

Example 4

Explain why writing IM to represent the number 999 is completely incorrect, and show the correct way to write it.

solution :

Step 1: Apply the strict combination rules of subtraction.

The symbol I can only be subtracted from V and X. It cannot be placed before any larger symbols like L, C, D, or M. Therefore, IM is an invalid combination.

Step 2: Break 999 down into separate valid place value parts to convert it properly.

999 = 900 + 90 + 9

Step 3: Convert each separate component according to valid rules.

900 = CM (1,000 − 100)
90 = XC (100 − 10)
9 = IX (10 − 1)

Step 4: Join the valid symbols together.

CM + XC + IX = CMXCIX

Final Answer = CMXCIX

Example 5

A student reads a historical book and notices a building with construction year markings that say MDCCCXCII. What year was this building completed?

solution :

Step 1: Read the complete symbol sequence from left to right and break it down by sizes.

M: One thousand = 1,000
DCCC: Five hundred plus three hundreds = 500 + 100 + 100 + 100 = 800
XC: Smaller value X is before larger C. Subtract: 100 − 10 = 90
II: Two ones combined = 1 + 1 = 2

Step 2: Add all the values together to find the final regular year value.

Year = 1,000 + 800 + 90 + 2 = 1,892

Final Answer = 1,892

Sample Questions

Attempt the following Questions:

(1.) Convert the regular number 647 into Roman numerals.

(2.) Convert the Roman numeral string MCCXLVI into a regular number.

(3.) Calculate the answer and express it as a Roman numeral: CCXCV + LXVIII

(4.) Identify why the Roman numeral combination "LL" is invalid, and state what number it is likely trying to represent.

(5.) A classic film shows the year MCMXXXIV in its opening credits. What regular calendar year does this represent?

Check The Answers Below:

Take Note:

No Number Zero: There is no symbol for the number 0 in Roman numerals. The ancient Romans did not have a character to represent nothing.
Never Repeat V, L, or D: You can repeat the symbols I, X, C, and M up to three times in a row. However, you can never write V, L, or D more than once next to each other.
Left Means Less: Placing a smaller symbol to the left of a larger symbol means you must subtract it. For example, IV means 5 minus 1, which equals 4.
Right Means More: Placing a smaller symbol to the right of a larger symbol means you must add it. For example, VI means 5 plus 1, which equals 6.
Strict Subtraction Pairs: You can only subtract I from V or X. You can only subtract X from L or C. You can only subtract C from D or M. This means you can never write shortcuts like IC for 99.

ROMAN NUMERALS

Basic Roman Numeral Symbols

Roman Numeral Reference Chart (1 to 1000)

Rules for Writing Roman Numerals

1. Rule of Repetition

2. Rule of Addition

3. Rule of Subtraction

4. Invalid Combinations and Subtraction Restrictions

Conversions and Operations

1. Converting Regular Numbers to Roman Numerals

2. Converting Roman Numerals to Regular Numbers

3. Addition and Subtraction Using Roman Numerals

Worked Examples

Sample Questions

Check The Answers Below:

Answers:

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