Roman NumeralsAn Introduction

Why Roman NumbersO Comparing and contrasting our number

system* with another helps us recognize and appreciate the richness and power of our number system.

O Converting between the two offers great practice in computing and pattern recognition.

* Our number system is called the Hindu-Arabic System

The Roman Numerals

Roman Number

Hindu-Arabic Number

I 1

V 5

X 10

L 50

C 100

D 500

M 1000

Roman numbers are made using the seven symbols as shown below:

The Roman NumeralsO Large numbers were written by putting a bar

over the symbol (or set of symbols) to make the number 1000 times larger. Examples:O indicates 5,000 O indicates 6,000O indicates 50,000 O indicates 50,000

O Our lesson will not deal with symbols with bars over them (i.e., all numbers in our lesson will be smaller than 5,000).

Writing a Roman Numeral

O Roman numbers are written by combining a subset of the seven numbers listed in the table.Examples: VII is 5 + 1 + 1 = 7. XIII is 10 + 1 + 1 + 1 = 13.

O If a smaller number comes before a larger number, you subtract the smaller from the larger. Examples: IV is 5 ̶ 1 = 4. IX is 10 ̶ 1 = 9.

Writing a Roman Numeral

O Only one digit is subtracted at one time. So, you can't represent 8 as IIX because that's subtracting one from ten twice. Rather, you'd write VIII. XLIV is considered adding (50 ̶ 10) to (5 ̶ 1), or 44, so that's okay.Examples: CIV is 100 + (5 ̶ 1) = 94. LIX is 50 + (10-1) = 59.

O The V is never subtracted. The number 45 is written as XLV, not VL.

Writing a Roman Numeral

O A number cannot be subtracted from another number that is ten (or more) times larger. So, I can't be subtracted from L; V can't be subtracted from C; and so forth. You'd never write 99 as CIC; it would be XCIX.

Example 1O What is the value of CDXLVI?

• C is 100 and D is 500. Since C is smaller than D, we subtract 100 from 500: 400.

• X is 10 and L is 50. Since X is smaller than L, we subtract 10 from 50: 40.

• V is 5 and I is 1. Since V is larger than I, we add 5 and 1: 6.

• Putting it all together, we get 400+40+6 = 446.

Example 2O How would you write 2346 as a Roman

numeral?O M is one-thousand so MM represents two-

thousand.O C is one-hundred so CCC represents three-

hundred.O L is fifty and X is ten so XL represents

forty.O V is five and I is one so VI represents six.O Putting it all together, we get MMCCCXLVI.

Time to PracticeO Use the interactives below to practice

converting from Roman numerals and to Roman Numerals.