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Roman numerals

Reading and writing the symbols up to M (1000).

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Long ago, the Romans wrote numbers with letters. You still see Roman numerals today: on clocks, in book chapters and at the end of film credits.

In this lesson you will learn:

the seven symbols and what each one is worth
the two rules: when to add and when to take away
how to write any number up to 1000 in Roman numerals
how to read Roman numerals back as ordinary numbers

1. The seven symbols

Key idea Roman numerals use just seven symbols. Every number is made by putting them together.

I	V	X	L	C	D	M
1	5	10	50	100	500	1,000

A way to remember I Value Xylophones Like Cows Do Milk. The first letters are the symbols in order, from smallest to biggest.

The symbols go 1, 5, 10, 50, 100, 500, 1000. Each one is either 5 times or 2 times the one before.
The Romans had no symbol for zero.

2. The two rules: add or take away

Rule 1: add When the symbols go from biggest to smallest, add them up. VI = 5 + 1 = 6. XVII = 10 + 5 + 1 + 1 = 17.

I, X, C and M can be used up to three times in a row: III = 3, XXX = 30, CCC = 300.
V, L and D are never used twice in a row. VV would just be X.

Rule 2: take away When a smaller symbol comes before a bigger one, take it away. IV = 5 − 1 = 4. IX = 10 − 1 = 9.

Only these six pairs take away. Learn them:

IV	IX	XL	XC	CD	CM
4	9	40	90	400	900

Watch out 4 is IV, not IIII. And you can only take away I, X or C, from the next two symbols up. So 99 is not IC.

3. Writing a number in Roman numerals

Key idea Split the number into hundreds, tens and ones. Write each part in Roman numerals, then join them up in that order.

The same pattern repeats in every column. Only the symbols change:

Digit	Ones	Tens	Hundreds
1	I	X	C
2	II	XX	CC
3	III	XXX	CCC
4	IV	XL	CD
5	V	L	D
6	VI	LX	DC
7	VII	LXX	DCC
8	VIII	LXXX	DCCC
9	IX	XC	CM

Example: write 594 in Roman numerals

Split it: 594 = 500 + 90 + 4.
Write each part: 500 = D, 90 = XC, 4 = IV.
Join them up: D + XC + IV = DXCIV.

AnswerDXCIV

Watch out Always split first. 99 = 90 + 9 = XC + IX = XCIX. A shortcut like IC is wrong.

4. Reading Roman numerals

Key idea Read from the left. Look out for a smaller symbol in front of a bigger one: that pair is one of the six take-away pairs.

Example: what number is CDXLVII?

CD is a pair: 500 − 100 = 400.
XL is a pair: 50 − 10 = 40.
VII = 5 + 1 + 1 = 7.
400 + 40 + 7 = 447.

Answer447

The mistakes that cost marks

Using four of the same symbol. 4 is not IIII and 40 is not XXXX. use a take-away pair: IV = 4, XL = 40.
Making up a take-away pair. 99 is not IC and 49 is not IL. split first: 99 = 90 + 9 = XCIX, and 49 = 40 + 9 = XLIX.
Adding a pair instead of taking away. XL is not 60. the smaller symbol is in front, so take away: 50 − 10 = 40.
Repeating V, L or D. VV is not how the Romans wrote 10. use the symbol for that number: X.
Mixing up D and M, or L and C. say the rhyme: I Value Xylophones Like Cows Do Milk. L = 50, C = 100, D = 500, M = 1000.

Quick checklist

Tick each one when you can do it without help.

I know the seven symbols: I, V, X, L, C, D and M.
I know when to add and when to take away.
I know the six take-away pairs: IV, IX, XL, XC, CD and CM.
I can write a number like 594 as DXCIV.
I can read a numeral like CDXLVII as 447.
I can spot a Roman numeral that is written wrongly.

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