Concept 5 of 7
Roman Numerals: All the Way to M
Today's big idea
Seven letters only, and a smaller one placed before a bigger one means subtract.
Only I, X and C are ever subtracted, so 45 is XLV and never VL.
How it works
👀 What's going on?
Roman numerals turn up on clock faces, book chapters and building dates, and they run on rules nothing else uses. There are only seven letters, and almost all of the difficulty is in one of them.
💡 Here's the trick
Look at the letters above. I, V, X, L, C, D and M stand for 1, 5, 10, 50, 100, 500 and 1000. Letters are added going left to right, except that a smaller letter placed before a bigger one is taken away instead.
🪄 How to do it
- 1.Read the letters above from left to right.
- 2.Wherever a smaller letter sits before a bigger one, subtract it from that bigger one.
- 3.Add all the resulting pieces together.
✍️ Try it
Write 1476 in Roman numerals. Then work out what DCXCIV is.
1476 splits into 1000, 400, 70 and 6, giving MCDLXXVI. DCXCIV is 500 plus 100, then 90, then 4, which makes 694.
⚠️ Watch out
You might be thinking any smaller letter can sit before any bigger one. Only I, X and C are ever subtracted, and only from the next two symbols up. That is why 45 is XLV and never VL, and why 99 is XCIX rather than IC.
🌟 Why this matters
Clock faces, film credits, monarch names and the dates carved on old buildings all use these. It is a reading skill you will need long after the exam.
Exam tip: Break the number into thousands, hundreds, tens and ones first, then convert each piece on its own.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What number is CMXLIV?”
- 1
Spot the subtractive pairs
CM = 900 (C before M) · XL = 40 (X before L) · IV = 4 (I before V). 🏛️
- 2
Add the pieces
900 + 40 + 4
- 3
Total
= 944
- 4
Answer ✓
CMXLIV = 944
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Split into value blocks and add. Subtractive pairs: CM=900, CD=400, XC=90, IV=4.
DECODE · ROUND 1 OF 3
Quick check
✅ VERIFICATION
Which of these is NOT a valid Roman numeral?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Rounding Big Numbers
Peek at the next digit, 5 up, 4 down.