Roman Numerals
Roman numerals write numbers with seven letters: I, V, X, L, C, D and M. This NSW Year 7 maths subtopic consolidates primary-school skills and has no Stage 4 outcome, but it is a good test of place value and careful reading.
You will read numerals by adding symbol values, spot subtractive pairs such as IV, IX, XL and CM, write numbers and years in Roman form, and calculate with them by converting, working and converting back. Clock faces, Olympic Games numbers and foundation stones all use them, and some clocks still show 4 as IIII. It is part of Year 7 Whole Numbers.
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.