# Pharmacy Tech Math | How to Use Roman Numerals

Jan 9th, 2020**Introduction**

**As part of the PTCB exam, candidates are expected to have a rounded knowledge of math; both basic and pharmacy-specific related math knowledge. Today, we review the basic pharmacy tech math that you need to know.**

Below, we review the distinction between Roman and Arabic numerals, and why it’s important to know this distinction.

We discuss the differences between Roman and Arabic numerals and detail how these values play an important role in the pharmacy setting.

Next, we review the fundamental rules that govern how to interpret Roman numerals. These are the vital rules that always get tested on the PTCB exam.

Finally, we review some **sample pharmacy tech math questions** to test your knowledge of what we have learned.

**Let’s get started.**

**Roman and Arabic Numerals**

Roman numbers – such as I, II, III, IV, and X etc. – are commonly used throughout the formulation of a description, often denoting how much of a medicine needs to be prescribed. For example: “III tabs” refers to “three tablets”, and so on.

Arabic numbers are what we are standardly accustomed to – numbers such as 10, 50, 7, and 98.

There are 7 letters used to denote Roman numbers: I, V, X, L, C, D, M. See the table below to learn what value is associated with each letter.

Arabic Number |
Roman Numeral |
---|---|

1 | I |

5 | V |

10 | X |

50 | L |

100 | C |

500 | D |

1000 | M |

We can see that X has a value of 10, C of 100, and so forth. Knowing these values is very important. After all, prescriptions use Roman numerals to denote quantities ordered.

Bear in mind that lower case Roman numerals are identical in value to higher case Roman numerals. For example: iii is the same as III; c is the same as C, and so on.

Next, we need to learn some simple rules about how Roman numerals are used:

**Standardly, when one Roman numeral is used after another, the total of both is taken:**

I = 1, II = 2, III = 3

No more than 3 of the same letter is used in succession. For example, we cannot have IIII. Instead, it would be IV (see below).

**When you place a smaller Roman numeral before a larger Roman numeral, we must subtract the smaller value from the higher value:**

IX = 1 taken from 10 = 9

IV = 1 taken from 5 = 4

CD = 100 taken from 500 = 400

**When you place a smaller Roman after a larger Roman numeral, you add the smaller numeral to the larger numeral:**

XI = 1 to be added to 10 = 11

VII = 2 to be added to 5 = 7

MD = 500 to be added to 1,000 = 1,500

**Finally, when a smaller Roman numeral is sandwiched between two larger Roman numeral values, we first do the subtraction step, before finally doing the addition step:**

XIX = X + (1 taken from 10) = X + 9 = 10 + 9 = 19

XXIV = XX + (1 taken from 5) = 10 + 10 + 4 = 24

Note that we are identifying the subtraction step and, once completed, we complete all addition steps to find the total.

Though it may seem strange to use the Latin “Roman” system in prescriptions, it remains the most widespread means through which prescription quantities are denoted. During the PTCB exam, candidates are asked to interpret prescriptions and, as part of this, candidates must know how to interpret Roman numerals.

Now that we have reviewed the fundamental rules, take a few minutes to test your knowledge with the sample PTCB questions below.

**Sample PTCB Questions**

Explained answers can be found below.

**Question 1**

**What is the Arabic number of the following Roman numeral – CXXIX?**

- 89
- 112
- 129
- 131

**Question 2**

**What is the Arabic number of the following Roman numeral – LXXXVIII?**

- 88
- 108
- 138
- 318

**Question 3**

**What is the Arabic number of the following Roman numeral – XIX?**

- 17
- 18
- 19
- 21

**Question 4**

**In the following prescription, how many tablets should be dispensed?**

**iv tabs x 3d po ud**

- 4
- 6
- 12
- 18

**Question 5**

**What quantity of drug (in grams) should be dispensed from the following prescription?**

**Ampicillin 250mg; qty XIV tabs**

- 0.75g
- 1.5g
- 2.25g
- 3.5g

**Answers**

Let’s look at how to solve each of the above 5 sample questions.

**Question 1 – Correct Answer: c. 129**

CXXIX

First, we identify the subtraction step – which is IX (1 taken from 10 = 9).

Now, we can complete the addition steps:

CXX + 9 = 100 + 10 + 10 + 9 = 129

**Question 2 – Correct Answer: a. 88**

LXXXVIII

A straightforward case of addition:

50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 88

**Question 3 – Correct Answer: c. 19**

XIX

This is another case where we must identify the subtraction step. Once we know this, the calculation becomes straightforward.

XIX = (10 + 1 taken from 10) = 10 + 9 = 19

Remember: once a lower numeral is before a higher numeral, we must subtract the lower numeral from the higher numeral.

**Question 4 – Correct Answer: c. 12**

iv tabs x 3d po ud

Translation: 4 tablets to be taken orally for 3 days, as directed.

Therefore, 12 tablets need to be dispensed to the patient.

**Question 5 – Correct Answer: d. 3.5g**

Ampicillin 250mg; qty XIV tabs

XIV = X + (1 taken from 5) = 10 + 4 = 14 tablets need to be dispensed

Each tablet contains 250mg.

14 x 250mg = 3,500mg

The question asks for the answer in grams: 3,500mg / 100 = 3.5 grams.

**Conclusion**

Pharmacy technicians are expected to safely and accurately interpret prescriptions. This means having a solid understanding of Roman numerals, what each letter means and how to convert Roman numerals into the Arabic equivalent.

This is important. In the interests of patient safety, the correct amount of drug must be dispensed to the patient. As a qualified pharmacy technician, it is incumbent upon you to know these details and to meet your professional duty.

**If you would like to practice more pharmacy tech math questions, become a registered member of PTCB Test Prep. There, in the learning platform, you have access to hundreds of questions and explained sample answers to help you master this and every other part of the pharmacy technician exam. At PTCB Test Prep, we get you ready.**