Roman Numerals
Every question with a fully worked solution.
- Roman Numerals - Video - How to Read Roman Numerals Watch
Theory
Roman numerals write numbers with seven letters: I, V, X, L, C, D and M. Add the values of the symbols, except when a smaller symbol comes just before a larger one: then subtract it (IV \(= 4\)). This Year 7 maths page shows how to read and write Roman numerals, including years.
Adding. When the symbols go from largest to smallest, add them: CLXI \(= 100 + 50 + 10 + 1 = 161\).
Subtractive pairs. A smaller symbol written just before a larger one is subtracted. There are only six pairs: IV \(= 4\), IX \(= 9\), XL \(= 40\), XC \(= 90\), CD \(= 400\), CM \(= 900\).
Reading. Look for the subtractive pairs first, then add all the parts: CXLIV \(= 100 + 40 + 4 = 144\).
Writing. Split the number into place values (thousands, hundreds, tens, ones), then write each part, largest first: \(694 = 600 + 90 + 4 =\) DC \(+\) XC \(+\) IV \(=\) DCXCIV.
Rules. A symbol is used at most three times in a row: \(3 =\) III, but \(4 =\) IV. V, L and D are never repeated and never subtracted. Many clocks write \(4\) as IIII instead of IV.
The symbols:
| Symbol | Value | Symbol | Value |
|---|---|---|---|
| I | \(1\) | C | \(100\) |
| V | \(5\) | D | \(500\) |
| X | \(10\) | M | \(1000\) |
| L | \(50\) |
| Digit | Ones | Tens | 100s | 1000s |
|---|---|---|---|---|
| \(1\) | I | X | C | M |
| \(2\) | II | XX | CC | MM |
| \(3\) | III | XXX | CCC | MMM |
| \(4\) | IV | XL | CD | |
| \(5\) | V | L | D | |
| \(6\) | VI | LX | DC | |
| \(7\) | VII | LXX | DCC | |
| \(8\) | VIII | LXXX | DCCC | |
| \(9\) | IX | XC | CM |
How to write a number in Roman numerals
- Split it into thousands, hundreds, tens and ones.
- Write each part from the table.
- Join the parts, largest first.
How to read a Roman numeral
- Find the subtractive pairs.
- Write the value of each pair and each other symbol.
- Add all the parts.
\(44 = 40 + 4 =\) XL \(+\) IV \(=\) XLIV
| \(1905\) | \(=\) | \(1000 + 900 + 5\) |
| \(1788\) | \(=\) | \(1000 + 700 + 80 + 8\) |
\(1905 =\) M \(+\) CM \(+\) V \(=\) MCMV
\(1788 =\) M \(+\) DCC \(+\) LXXX \(+\) VIII \(=\) MDCCLXXXVIII
(i) LXVIII
(ii) MMXXII
(iii) DCCXV
| \(60 + 8\) | \(=\) | \(68\) |
| \(2000 + 20 + 2\) | \(=\) | \(2022\) |
| \(500 + 200 + 15\) | \(=\) | \(715\) |
(i) LX \(+\) VIII \(= 68\)
(ii) MM \(+\) XX \(+\) II \(= 2022\)
(iii) D \(+\) CC \(+\) XV \(= 715\)
| \(400 + 90 + 4\) | \(=\) | \(494\) |
CD \(= 500 - 100 = 400\), XC \(= 100 - 10 = 90\), IV \(= 5 - 1 = 4\). CDXCIV \(= 494\).
| \(1000 + 900 + 30 + 2\) | \(=\) | \(1932\) |
| \(1000 + 900 + 70 + 3\) | \(=\) | \(1973\) |
| \(1973 - 1932\) | \(=\) | \(41\) |
\(41 = 40 + 1 =\) XLI years apart.
Check each numeral: V, VI, VII and VIII each contain one V; IIII and IX do not. So V appears \(4\) times.
Common pitfalls
Frequently asked questions
What are the seven Roman numeral symbols?
I (1), V (5), X (10), L (50), C (100), D (500) and M (1000).
Why is 4 written IV?
I before V means 5 take away 1.
What are the subtractive pairs?
IV, IX, XL, XC, CD and CM.
How do you write a year in Roman numerals?
Split it into thousands, hundreds, tens and ones and write each part.
Why do some clocks show IIII?
It is a clock-making tradition; IIII and IV both mean 4.