Measuring

# Lesson

Learning Outcomes

By the end of this chapter, learners will be able to:

• describe the Roman numeral system,
• convert Roman numerals to Arabic numbers, and
• convert Arabic numbers to Roman numerals.

## The Roman Numeral System

The basic Roman numeral system is made up of seven letters which represent numerical values. Either upper or lowercase letters can be used. Although not used extensively in the healthcare system, there are situations which arise where Roman numerals are used instead of typical Arabic numbers. Can you think of any instances where you have seen Roman numerals used in healthcare?

Table 9.1 Roman Numeral Values
Roman Numeral Arabic Number
I 1
V 5
X 10
L 50
C 100
D 500
M 1,000

## Interpreting Values of Roman Numerals

Numbers outside of the values above are represented by using these letters in combination. The combinations can have multiple letters in a row, but always follow a particular pattern.

• You add the values of the letters together when they are the same letter or the letter values are in descending order.
• This pattern is used for all numbers except those including 4 and 9.
• Examples:
• XX (10+10) = 20
• MCCLXXXVIII (1000+100+100+50+10+10+10+5+1+1+1) = 1,288
• For values that include 4 and 9, one must use subtraction of values to determine the number being represented.
• When a lower value letter is to the left of a higher value letter, subtract it from the letter to the right.
• If a lower value letter is between two large value letters, subtract it from the letter to the right.
• Examples:
• IV (5-1) = 4
• XLIV [(50-10)+(5-1)] = 44
• If a line is drawn above a letter, multiply the numeral by 1,000, however it is very unlikely you will see any Roman numerals written in this form in the context of nursing work.

What is the numerical value of XXI?

First, determine each of the letter values: 10 , 10 , 1

Second, determine if the letters should be added or subtracted.  To do this, identify if a lower value letter is to the left of any of the values. If it is, subtract the lower value from the value to the right, then add the remaining values.

In this case, all values to the left of 1 are higher, therefore you can just add all the values together.

10 + 10 + 1 = 21
XXI = 21

Sample Exercise 9.1

What is the numerical value of XXIV?

XXIV = 24

1. Determine the values of each letter: 10, 10, 1, 5
2. Identify if a lower value is to the left of a larger value: 1 is to the left of 5.
3. Subtract the lower value from the larger value: 5 – 1 = 4
4. Add this number to the remaining numbers: 10 + 10 + 4 = 24

## Writing Arabic Numbers as Roman Numerals

When writing numbers, you should follow the rules written in the section above and also note there should never be more than three of the same letter in a row.

How do you write the Arabic number 71 as a Roman numeral?

Generally*, start by using the biggest value Roman numeral without going over the Arabic number: L = 50

Sometimes it can be helpful to count as you add the letters in a row: L 50, LX 60, LXX 70, LXXI 71

*Note that in some cases, particularly with numbers ending in 9, you may start with a numeral with a value greater than the final Arabic number.

Sample Exercise 9.2

How do you write the Arabic number 53 as a Roman numeral?

LIII

1. Identify the Roman numeral with the biggest value without going over: L
2. Add additional letters to obtain the correct numerical value: 50 + 1 + 1 + 1 = 53

# Practice Set 9.1: Converting Roman Numerals to Arabic Numbers

Practice Set 9.1: Converting Roman Numerals to Arabic Numbers

Convert the following Roman numerals into Arabic numbers.

1. XX
2. VI
3. VIII
4. IV
5. IX
6. XXVII
7. II
8. M
9. LV
10. CXXV
1. 20
2. 6
3. 8
4. 4
5. 9
6. 27
7. 2
8. 1,000
9. 55
10. 125

# Practice Set 9.2: Converting Arabic Numbers to Roman Numerals

Practice Set 9.2: Converting Arabic Numbers to Roman Numerals

Convert the following Arabic numbers to Roman numerals.

1. 36
2. 21
3. 7
4. 18
5. 14
6. 49
7. 86
8. 35
9. 3
10. 12
1. XXXVI
2. XXI
3. VII
4. XVIII
5. XIV
6. IL
7. LXXXVI
8. XXXV
9. III
10. XII