Roman numerals use symbols to represent numbers, with I=1, V=5, X=10, L=50, C=100, D=500, and M=1000. Numbers are written by combining symbols, with smaller values subtracted from larger ones to the left. For example, IV=4 and IX=9. Only one digit can be subtracted at a time. Roman numerals cannot have a number subtracted that is more than 10 times larger. Practice problems are provided to convert between Hindu-Arabic and Roman numerals.

1. Roman Numerals
An Introduction

2. Why Roman Numbers
O 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

3. 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:

4. The Roman Numerals
O

5. 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.

6. 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.

7. 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.

8. Example 1
O 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.

9. Example 2
O 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.

10. Time to Practice
O Use the interactives below to practice
converting from Roman numerals and to
Roman Numerals.