Math 409/409GHistory of Mathematics

Roman Numerals

No doubt, you all remember them. They’re displayed at the right. But do you remember how to use them?

The Roman numeration system is essentially additive with some subtractive and multiplicative properties thrown in.

1 I

5 V

10 X

50 L

100 C

500 D

1000 M

Examples

Additive 11 is 1 after 10

Subtractive9 is 1 before 10

Multiplicative

9 10 1 IX

11 10 1 XI

15,000 15 1000 XV

Roman numeral additive rule

If the Roman symbols decrease in value from left to right or the number in our system does not contain 4’s or 9’s, their values are added. Examples:

D 500MM XC XXC 2II 2 0000 27370V 30 25

501268 10100 520 3 IIV0 I0 C XLMC

50 L

10

5

0 C

5

10

00

1

D

1

V

I

X

000 M

Roman numeral subtractive rule

For numbers involving 4’s or 9’s, the letter of the smaller unit is placed before the higher unit. Examples:

4 = 5 – 1 = IV

9 = 10 – 1 = IX

40 = 50 – 10 = XL

90 = 100 – 10 = XC

400 = 500 – 100 = CD

900 = 1000 – 100 = CM

The Roman numeral subtractive rule for numbers involving 4’s and 9’s requires that:

I comes before only V or X.

X comes before only L or C.

C comes before only D or M.

Examples:1 I

5 V

10 X

50 L

100 C

500 D

1000 M

400

CD

90

XC

2

II

X

149

IX 2V 4

2 1000

= 0C 00

M

1

Roman numeral multiplicative rule

To multiply a Roman numeral by 1000, place a bar on top of it; to multiply it by 10002, place a double bar on top. Examples:

2

9 IX

920 CMX

1000

1000

CCX

14,920,000

DLXVII 567

1,234,56

1000

I 1,000,000XXIV 234,00

900

14 IV

7

0

0

X X

This ends the lesson on

Roman Numerals