Concept 6 of 6
Roman Numerals: Letters That Count
Today's big idea
Seven letters stand for numbers: add them as you read left to right, but subtract any smaller letter that comes first.
XXVII is 10 + 10 + 5 + 1 + 1 = 27. In XL the smaller X comes first, so it is 50 - 10 = 40.
How it works
👀 What's going on?
Look at the clock on a classroom wall or a station platform and you may find no digits on it at all. Where you expect a 4 there is IV, where you expect a 9 there is IX, and 12 is written XII. The same thing turns up on the cornerstone of an old building, in the name of a king like Henry VIII, at the top of book chapters, and in the year at the end of a film.
These are Roman numerals, and people wrote numbers this way for over a thousand years before the digits you use were invented. Two things about the system are worth knowing before you read a single one. There are only seven letters in the whole of it, so there is far less to learn than it looks. And there is no zero at all, which means there are no rooms holding place value the way 3,482 has a thousands room and a tens room. In Roman numerals the letters carry the value themselves, so where a letter sits does not change what it is worth. It only changes whether you add it or take it away.
💡 Here's the trick
Look at the seven chips above. Each letter is worth the same amount every single time it appears: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1,000. An X is worth 10 whether it stands at the front or the back. That is the opposite of the 3 in 3,482, which is worth 3,000 only because of the room it sits in.
Most of the time you simply read left to right and keep a running total in your head. XXVII is X + X + V + I + I, so 10 + 10 + 5 + 1 + 1 = 27. Biggest letters first, smaller ones after, adding as you go.
There is one exception, and it exists to save writing. Rather than put the same letter down four times in a row, the Romans wrote a smaller letter in front of a bigger one to mean take this away. XLIV splits into two pairs: XL is 50 - 10 = 40, and IV is 5 - 1 = 4, so the whole thing is 44. The signal never changes. If a letter is smaller than the one straight after it, subtract it instead of adding it.
🪄 How to do it
- 1.Read the letters left to right, taking each value from the picture above.
- 2.If a letter is smaller than the one straight after it, subtract it.
- 3.Otherwise add it, then total everything up.
✍️ Try it
What number is XCIX? Both of its pairs are subtractions, so take them one pair at a time.
Split it into XC and IX. In XC the X is smaller than the C, so that pair is 100 - 10 = 90. In IX the I is smaller than the X, so that pair is 10 - 1 = 9. Together they make 99.
⚠️ Watch out
You might be thinking any smaller letter can sit in front of any bigger one, so 99 could be written IC. It cannot. Only I, X and C are ever subtracted, and never from more than two letters up. A letter also never repeats more than three times, which is why 40 is XL and not XXXX.
🌟 Why this matters
Roman numerals still turn up on clock faces, film credits, book chapters and the dates carved into buildings. Working out the year on an old monument is a small pleasure that needs exactly this skill.
Exam tip: Almost every paper carries one Roman numeral question, and it is usually the quickest mark available.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What number is XLII?”
- 1
Break it into letters
X, L, I, I. Look at neighbours.
- 2
Check for subtract trick
X (10) sits before L (50). Smaller before bigger → subtract: XL = 50 − 10 = 40.
- 3
Add the rest
II = 1 + 1 = 2.
- 4
Sum it ✓
XLII = 40 + 2 = 42
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap letters to build numbers. Big letter before small = ADD. Small letter before big = SUBTRACT.
TARGET · ROUND 1 OF 3
7
Build this in Roman.
Your Numeral
Decoded value: —
Quick check
✅ VERIFICATION
What number does XXIX represent?
⚡ Finish the activity above first to answer.
Keep going!