Roman numerals

The idea

Roman numerals use the landmark symbols I, V, X, L, C, D, M for 1, 5, 10, 50, 100, 500, 1000, writing 4 as IV (1 less than 5) and 40 as XL (10 less than 50).

Four marks for 4?

Written the plain way, 4 is IIII and 40 is XXXX: four marks each. But 4 is just 1 less than 5, and 40 is 10 less than 50.

How might you write 4 with only two symbols?

• I then V
• V then I
• I then I

Write in Roman numerals

Tap the symbols to write each number. The toy shows what your numeral is worth.

Seven symbols, and one less than

Roman numerals use the landmark symbols I, V, X, L, C, D, M for 1, 5, 10, 50, 100, 500, 1000, writing 4 as IV (1 less than 5) and 40 as XL (10 less than 50).

I = 1 · V = 5 · X = 10 · L = 50 · C = 100 · D = 500 · M = 1000

IV = 5 − 1 = 4 · XL = 50 − 10 = 40 A smaller symbol before a bigger one is taken away.

Notes

Roman numerals use the landmark symbols I, V, X, L, C, D, M for 1, 5, 10, 50, 100, 500, 1000, writing 4 as IV (1 less than 5) and 40 as XL (10 less than 50).

Check yourself

Which is the Roman numeral for 40?

What number is XXIV?

Answer: 24

XXIV = 10 + 10 + (5 − 1) = 24.

What number is DCXLV?

Answer: 645

DCXLV = 500 + 100 + (50 − 10) + 5 = 645.

What is the difference between VI and IV?

• XL — correct. Yes! X before L means 10 less than 50.
• LX. LX is L then X: 50 + 10 = 60. The small symbol must come before the big one to be taken away.
• XC. XC is 10 less than 100, which is 90.
• VI = 5 + 1 = 6 and IV = 5 − 1 = 4 — correct. Yes! A smaller symbol before a bigger one is taken away; after it, it is added.
• Both are 6. IV has the small symbol before the big one, so it is taken away: 5 − 1 = 4.
• VI = 4 and IV = 6. It is the other way round: VI = 5 + 1 = 6 and IV = 5 − 1 = 4.