6 Roman Numerals
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
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? Modern medicine uses Roman numerals in prescribing medications, especially when using apothecaries’ system of measurement. They can also be used to identify controlled substances, writing medications in small dose increments, and when ordering supplies.
The basic Roman numeral system is made up of seven letters which represent numerical values. Either upper or lowercase letters can be used.
| 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:
[latex]XX (10+10) = 20[/latex]
[latex]MCCLXXXVIII (1000+100+100+50+10+10+10+5+1+1+1) = 1,288[/latex]
- 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:
[latex]IV (5-1) = 4[/latex]
[latex]XLIV [(50-10)+(5-1)] = 44[/latex]
- No letter will repeat itself more than three times.
- Examples:
[latex]I, II, III, IV, V, VI, VII, VIII, IX (1, 2, 3, 4, 5, 6, 7, 8, 9)[/latex]
[latex]X, XX, XXX, XL (10, 20, 30, 40)[/latex]
[latex]XXXIII, XXXIV (33, 34)[/latex]
- Examples:
Example
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.
[latex]10 + 10 + 1 = 21[/latex]
[latex]XXI = 21[/latex]
Sample Exercise 6.1.
What is the numerical value of XXIV?
Answer:
[latex]XXIV = 24[/latex]
- Determine the values of each letter: 10, 10, 1, 5
- Identify if a lower value is to the left of a larger value: 1 is to the left of 5.
- Subtract the lower value from the larger value: [latex]5 - 1 = 4[/latex]
- Add this number to the remaining numbers: [latex]10 + 10 + 4 = 24[/latex]
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: [latex]L = 50[\latex]
- Next, add additional letters until the values add up to the correct numerical value: [latex]LXXI (50+10+10+1=71)[/latex]
- 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 6.2
How do you write the Arabic number 53 as a Roman numeral?
Answer:
LIII
- Identify the Roman numeral with the biggest value without going over: L
- Add additional letters to obtain the correct numerical value: [latex]50 + 1 + 1 + 1 = 53[/latex]
Practice Set 6.3 Converting Roman Numerals to Arabic Numbers
Convert the following Roman numerals into Arabic numbers.
- XX
- VI
- VIII
- IV
- IX
- XXVII
- II
- M
- LV
- CXXV
Answers:
- 20
- 6
- 8
- 4
- 9
- 27
- 2
- 1,000
- 55
- 125
Practice Set 6.4 Converting Arabic Numbers to Roman Numerals
Convert the following Arabic numbers to Roman numerals.
- 36
- 21
- 7
- 18
- 14
- 49
- 86
- 35
- 3
- 12
Answers:
- XXXVI
- XXI
- VII
- XVIII
- XIV
- IL
- LXXXVI
- XXXV
- III
- XII
Case Studies
Scenario A: Medication Scheduling Using Roman Numerals
Sarah, a 65-year-old from Cape Breton, Nova Scotia, has been prescribed Lasix (furosemide) to manage her congestive heart failure. She needs to take Lasix every VIII (8) hours. She takes her first dose at 6 AM.
Question: Using Roman numerals, what time will Sarah take her third dose?
Answer
Answer: Sarah will take her third dose at XXII hours (10 PM).
Scenario A Solution:
Sarah takes Lasix every VIII (8) hours.
- First dose: 6 AM
- Second dose: [latex]6 AM + 8 \text{ hours } = 2 PM[/latex]
- Third dose: [latex]2 PM + 8 \text{ hours } = 10 PM[/latex]
In Roman numerals, 10 PM is written as:
- XXII (10 PM).
Scenario B: Dosage Calculation Using Roman Numerals
John, a 72-year-old patient from Halifax, Nova Scotia, has been diagnosed with chronic obstructive pulmonary disease (COPD). His doctor has prescribed a medication called Symbicort to be administered twice daily. The prescription states that he should take IV (4) puffs of Symbicort daily, with each puff delivering 80 micrograms of the drug.
Question: If John takes the prescribed amount, how many micrograms of Symbicort will he take in one day? Express the daily dosage using Roman numerals.
Answer
Answer: John will take CCCXX micrograms of Symbicort in one day.
Scenario B Solution:
John takes IV (4) puffs each day, and each puff delivers 80 micrograms of Symbicort.
- [latex]\text{ Daily dosage } = 4 \text{ puffs } × 80 \text{ micrograms } = 320 \text{ micrograms. }[/latex]
In Roman numerals, 320 is written as:
- [latex]CCCXX (300 + 20).[/latex]
Chapter Credit
Adapted from Chapter 9 Roman Numerals in A Guide for Numeracy in Nursing by Julia Langham, CC BY 4.0.
Case Studies are new content.
