1.1 Number Systems

Two types of number systems are used in pharmacy calculations: Arabic numbers and Roman numerals. The Arabic number system uses numbers, fractions, and decimals, whereas the Roman numeral system uses letters to represent quantities or amounts. The Arabic number system is more commonly used in the healthcare setting.

Understanding the Arabic Number System

The Arabic number system has its roots in India and consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When these digits are combined, they represent every possible number. In expressions using Arabic numbers, whole numbers are to the left of a decimal point, whereas fractions are to the right of a decimal point.

Understanding the Roman Numeral System

The Roman numeral system can be traced back to ancient Rome and includes seven main symbols: I (equal to 1), V (equal to 5), X (equal to 10), L (equal to 50), C (equal to 100), D (equal to 500), and M (equal to 1,000). Being able to interpret Roman numerals when used on prescriptions and medication orders is important for the accurate preparation and dispensing of medications (see Table 1.1).

images Work Wise

Pharmacy technicians should ask for clarification for any Arabic numbers or Roman numerals that are difficult to read or understand. Engaging in this confirmation process can help to prevent a medication error.

Roman numerals are expressed as either uppercase letters or lowercase letters. The most frequently used uppercase letters are the Roman numerals I, V, and X, which represent 1, 5, and 10, respectively. For example, tablet quantities of ampicillin may be written in uppercase letters, such as ampicillin 250 mg XXX tabs, indicating 30 tablets. The lowercase letter i is used to represent 1, the lowercase letter ii to represent 2, and so on. For example, aspirin gr images indicates 3 grains of aspirin. To prevent errors in interpretation, a line is drawn above the lowercase letters, with the dot above the line (for example: images, images, images). Another lowercase letter you may see in pharmacy practice is the lowercase letter s. For example, the abbreviation ss or images means ½.

Table 1.1 Guidelines for Interpreting Roman Numerals

  1. When a numeral is repeated or a smaller numeral follows a larger one, the numerals are added.

    II = 1 + 1 = 2

    VII = 5 + 1 + 1 = 7

    XXI = 10 + 10 + 1 = 21

    LVII = 50 + 5 + 1 + 1 = 57

    LXV = 50 + 10 + 5 = 65

    CXIII = 100 + 10 + 1 + 1 + 1 = 113

  1. When a smaller numeral comes before a larger numeral, the smaller numeral is subtracted from the larger numeral.

    IV = 5 − 1 = 4

    IX = 10 − 1 = 9

    CD = 500 − 100 = 400

  1. Numerals are never repeated more than three times in sequence.

    III = 3

    IV = 4

    XXX = 30

    XL = 40

  1. When a smaller numeral comes between two larger numerals, the smaller numeral is subtracted from the numeral that follows.

    XIX = 10 + (10 − 1) = 19

    XIV = 10 + (5 − 1) = 14

Table 1.2 compares commonly used Roman numerals and their equivalent Arabic numbers. The examples that follow the table show the use of Roman numerals in both dosing instructions and quantity to dispense.

Table 1.2 Comparison of Roman Numerals and Arabic Numbers

Roman Numeral

Arabic Number

ss or images

=

½ or 0.5

I or i or images

=

1

V or v

=

5

X or x

=

10

L or l

=

50

C or c*

=

100

D or d

=

500

M or m

=

1,000

*Be aware that cubic centimeter is abbreviated as cc. However, the use of this abbreviation is discouraged due to the risk of misinterpretation.

Example 1.1.1

A prescription is received in the pharmacy and includes the following notation: Disp: C tablets. How many tablets are to be dispensed?

Answer: The quantity of tablets to dispense is 100 tablets, indicated by the Roman numeral C.

Roman numerals may be grouped together to express different quantities. To interpret these numbers, addition and subtraction must be used, as specified in the guidelines shown in Table 1.1. Example 1.1.2 demonstrates how to read groups of Roman numerals.

Example 1.1.2

The following prescription is received in the pharmacy. How many tablets are in the ordered dose, and how many tablets are to be dispensed?

imagesDiphenhydramine XXV mg

Dosing instructions: Take images tablets by mouth each night.

images

Quantity to dispense: XXXII tablets

To begin, determine the number of tablets in the ordered dose that the patient will take each night.

image

Then calculate the number of tablets to dispense by adding the Roman numerals on the prescription.

XXXII tablets = 10 + 10 + 10 + 1 + 1 = 32 tablets

Answer: For this prescription, there are 2 tablets of diphenhydramine in the ordered dose, and 32 tablets must be dispensed.

images Name Exchange

Diphenhydramine is the generic name for Benadryl. The oral dosage form is an over-the-counter (OTC) medication, but the injectable dosage form requires a prescription.

1.1 Problem Set

Provide the equivalent Arabic number for each of the following Roman numerals.

  1. X

  2. V

  3. DCXXIV

  4. MML

  5. XLVIII

Provide the equivalent Roman numeral for each of the following Arabic numbers.

  1. 17

  2. 67

  3. 1,995

Solve the following problems and provide your answers in Roman numerals.

  1. 7 + 6 =

  2. 354 − 27 =

  3. 2 × 45 =

  4. 150 ÷ 2 =

Solve the following problems and provide your answers in Arabic numbers.

  1. VIIss + XV + IV =

  2. XLVII − XIX =

  3. XVII × IV =

  4. XLII ÷ III =

Applications

  1. A patient is to take “VIIss tablets three times daily.” How many tablets are to be taken at each dose?

  2. Using the prescription below, answer the following questions. Note: The abbreviation gr means “grains,” and the abbreviation po means “by mouth.”

    imagesAspirin gr X

    images

    Dosing instructions: images po daily

    Quantity to dispense: C

    1. What is the strength of the tablet?

    2. What is the daily dose?

    3. What is the quantity to be dispensed?

  3. Using the prescription below, answer the following questions. Note: The abbreviation po means “by mouth,” and the abbreviation TID means “three times a day.”

    images Erythromycin 250 mg

    Dosing instructions: images po TID with food

    images

    Quantity to dispense: XXVII

    1. How many tablets will be taken at each dose?

    2. How many days will the prescription last?

  4. Using the prescription below, answer the following questions. Note: The abbreviation po means “by mouth.”

    images Glipizide tablet 5 mg

    images po every morning

    images po with lunch

    images

    images po with dinner

    Quantity to dispense: CL

    1. How many tablets are taken each day?

    2. How many tablets will be dispensed?

Self-check your work in Appendix A.