Math and Dosage Calculations Module

Math and Dosage Calculations Module Level 1_rev.5/4/15 Page 1

South Texas College

Associate Degree in Nursing

RNSG 1362

Clinical 1

Math and Dosage Calculations Module


Table of Contents Page

I. Basic Math

A. Fractions 3

B. Decimals 4

II. Common Calculations 6

III. Common Medical Abbreviations

A. Frequency & Route of Drug Administration 7

B. Units of Measure, and General Abbreviations 8

IV. Systems of Measurement

A. Metric System 9

B. Household System 10

C. Apothecary System 11

D. Other Common Drug Measurements 12

V. Time 13

VI. Temperature 15

VII. Drug Dosage Calculations

A. Oral Dosage of Drugs 17

B. Parenteral Dosage of Drugs 19

C. Dosages Based on Body Weight 20


Module 1: Basic Math_______________________________________________

A. Fractions

A fraction indicates a portion of a whole number.

Example: 1

4 = 1 part of 4 parts, or

1

4 of the whole

Mixed Numbers:

When a whole number and a fraction are combined, the result is referred to as a

mixed number.

Example: 15

8 = 1 +

5

8

Reducing Fractions to the Lowest Terms:

When calculating dosages, it is usually easier to work with fractions using the smallest

possible numbers.

To reduce a fraction to lowest terms, divide both the numerator and denominator by the

largest non-zero whole number that will go evenly into both numerator and denominator.

Example:

Reduce 6

12 to lowest terms

6

12 =

6 ÷ 6

12 ÷ 6 =

1

2

Note:

For tablets if the value is less than a whole number always write it in fraction.

Example:

Correct: 1 ½ tablets

Wrong: 1.5 tablets


B. Decimals

Decimal numbers are numeric values that include a whole number, a decimal point, and a

decimal fraction.

No trailing zero

When writing decimals, eliminate unnecessary zeros at the end of the number to avoid

confusion. The Joint Commission forbids the use of trailing zeros for medication orders or

other medication-related documentation and cautions that, in such cases, the decimal point

maybe missed when unnecessary zero is written.

Example: Correct: 10

Wrong: 10.0 which can be misinterpreted as 100 if decimal point is not clear.

Always place a leading zero

Always write a zero to the left of the decimal point to emphasize that the number has a value

less than 1. The Joint Commission’s Official “Do Not Use” list prohibits writing a decimal

fraction that is less than 1 without a leading zero.

Example: Correct: 0.45

Wrong: .45 which can be misinterpreted as 45 if the decimal point is not clear

or if the decimal point is overlooked.

Whole

Numbers

Decimal

Fractions

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Rounding Decimal Numbers

Sometimes it is convenient to round an answer – that is, to use an approximate answer rather

than the exact one.

Rounding Off

To round off 1.267 to the 1st decimal place or 1st decimal number – do the following:

Look at the digit after the 1st decimal place (the number on the right or the number on the

2nd decimal place). Because this digit (6) is 5 or more, round off 1.267 by adding 1 to the

number on the 1st decimal place. Finally, drop all the digits after the 1st decimal place.

So, 1.267 is approximated by 1.3 when rounded off to the 1st decimal place/number.

To round off 0.8345 to the 2nd decimal place or 1st decimal number – do the following:

Look at the digit after the 2nd decimal place (the number to the right or the number on the

3rd decimal place). Because this digit (4) is less than 5, round off 0.8345 by leaving the

2nd decimal digit alone. Finally, drop all the digits after the 2nd decimal place.

So, 0.8345 is approximated by 0.83 when rounded off to the 2nd decimal place/number.

Practice Exercises:

1. Round off 3.547 to the 1st decimal place or 1st decimal number.

______________

2. Round off 3.547 to the 2 nd decimal place or 2 nd decimal number.

______________

3. Round off 3.547 to a whole number.

______________


Module II: Common Calculations______________________________________

Dosage: Formula Method

Step 1. Convert

Step 2. Think

Step 3. Calculate: Desired dose

Dose on hand x Quantity = unknown

Dosage: Ratio-Proportion Method

Step 1. Convert

Step 2. Think

Step 3. Calculate: Dosage on hand

Amount on hand =

Dosage desired

X Amount desired

Dosage: *Dimensional Analysis Method *highly recommended method to use

Step 1. Determine unit of measure for amount to give ratio for left side of equation

Step 2. Think

Step 3. Match unit of numerator of supply dosage ratio with the unit of numerator of

amount to give ratio. Set up all other ratios so units cancel, leaving unit of amount

to give. Calculate:

Amount Supply Conversion Ordered

to Give = Dosage x Factor x Dosage

Ratio Ratio Ratio Ratio


Module III: Common Medical Abbreviations____________________________

A.1. Frequency of Drug Administration

ac = before meals

ad lib = as desired, freely

hs = at bedtime, at hour of sleep

tid = three times a day

qid = four times a day

qh = every hour

q2h = every 2 hours

q3h = every 3 hours

q4h = every 4 hours

pc = after meals

prn = whenever needed, when necessary

stat = immediately, at once

A.2. Route of Drug Administration

HHN = Hand-held nebulizer

ID = Intradermal

IM = Intramuscular

IV = Intravenous

IVF = Intravenous Fluid

IVPB = Intravenous Piggyback

NGT = nasogastric tube

PEG = percutaneous endoscopic gastrostomy

po/PO = by mouth

pr/PR = per rectum

SL = Sublingual

Subcu = subcutaneous

Supp = suppository

Top = topical

od = right eye

os = left eye

ou = both eyes


B.1. Units of Measure

c = cup

cm = centimeters

ft = foot

g = grams

gr = grains

in = inches

kg = kilograms

L = liters

lb = pound

m = meters

mcg = micrograms

mEq = milliequivalents

mg = milligrams

mL = milliliters

mm = millimeters

oz = ounce

pt = pint

T /tbs = tablespoons

t/tsp = teaspoons

B.2. General

cap = capsule

ER = extended release

gtt = drop

NKA = no known allergy

NPO = nothing by mouth

SR = sustained release

susp = suspension

tab = tablet

XL/XR= extended release


Module IV: Systems of Measurement___________________________________

A. Metric System

Unit Abbreviation Equivalents

Weight gram (base unit)

milligram

microgram

kilogram

g

mg

mcg

kg

1 g = 1000 mg = 1000000 mcg

0.001 g = 1 mg = 1000 mcg

0.000001 g = 0.001 mg = 1 mcg

1 kg = 1000 g

Volume liter (base unit)

milliliter

L

mL

1 L = 1000 mL

0.001 L = 1 mL

Length

meter (base unit)

centimeter

millimeter

m

cm

mm

1 m = 100 cm = 1000 mm

0.01 m = 1 cm = 10 mm

0.001 m = 0.1 cm = 1 mm

Note: No commas on amounts at or above one thousand.

Example: Correct: 1000

Wrong: 1,000 which the comma can be misinterpreted as a decimal point if

not written legibly

Practice Exercises:

1. Change to the designated equivalents.

76 mg = ____________________ mcg


1.5L = ____________________ mL


3.36 cm = ____________________ mm


B. Household System

The household unit is likely used by patient at home where hospital measuring devices

are not usually available. You should be familiar with the household system of

measurement so that you can explain take-home prescriptions to your patient.

Equivalents

Household Measures

Metric Measures

1 t

5 mL

3 t

1 T 15 mL

2 T

1 fl oz 30 mL

1 cup

8 fl oz 240 mL

1 pint

2 cups or 16 fl oz 480 mL

1 lb

16 oz

2.2 lb

1 kg

1 in 2.54 cm

1 ft 12 in

Practice Exercises:

______ mL 1. The urinary output of a patient with an indwelling Foley catheter is 1.4 L.

How many milliliters of urine are in the bag?


______ mL 2. What is the patient’s total fluid intake in mL for the day if he had the following

fluid intake?

Breakfast = 8 oz. milk, 1 cup water

Lunch = 4 oz. juice, 3 T medication, ½ cup water

Dinner = 6 oz. soup, 12 oz soda, ½ cup water

______ oz. 3. The patient drank 720 mL of the laxative agent Colyte. How many ounces of

laxative did the patient drank?

___________________________________________________________________________

Example:

A patient needs to drink 1.5 oz. of an elixir per day. How many teaspoons would be

equivalent to this dose?

1.5 oz x 30 mL

1 oz x

1 tsp

5 mL =

45oz mL tsp

5 oz mL = 9 tsp

Practice Exercises:

______ tsp/s. 1. A patient is to take 5 mL of a medication. However, he will be using a teaspoon at

home. The nurse instructed the patient that dose will be equivalent to ____ tsp/s.


______ T 2. Order: Amoxil (amoxicillin) oral suspension 1tsp PO q8h. How many tablespoons

of Amoxil (amoxicillin) will the patient receive in 3 full days?

_______tsp 3. The order is indomethacin 75 mg PO daily in 3 divided doses. The label reads

indomethacin 25 mg per 5 mL. How many teaspoons should you administer

per dose?

Practice Exercises 4 and 5 refers to this scenario.

Scenario: A patient is given a prescription to take 15 mL of medication every 8 hours for 10

days. The patient will be using a household measuring device at home to measure

the dose of medication.

_____ tsp/s 4. How many teaspoon/s of medication will the patient take in one day?

_____ bottles 5. If the medication is supplied in a 0.5 L bottle, how many bottles will the patient

need to complete the 10 days of treatment?


Example:

Adam is 6 feet 3 inches tall. What is his height in centimeters?

6 ft x 12 in

ft = 72 in + 3 in = 75 in x

2.54 cm

in = 190.5 cm

______________________________________________________________________________

Practice Exercises:

_______ mm 1. A tumor has a diameter of 2 inches. What is the diameter of the tumor

measured in millimeters?

________ cm 2. A patient is 5 feet 9 inches tall. Find the height of the patient in centimeters.

(Round off your answer to the first decimal number/place.)

________in 3. A patient is 182 centimeters tall. Find the height of the patient in inches. (Round

off your answer to the second decimal number/place.)


Example:

Jennifer weighs 115 pounds 8 ounces. What is her weight in kilograms?

8 oz x 1 lb

16 oz =

8

16 lb = ½ lb = 0.5 lb

115 lb + 0.5 lb = 115.5 lb

115.5 lb x 1 kg

2.2 lbs =

115

2.2 kg = 52.5 kg

Practice Exercises:

_______ lb 1. A woman weighs 75 kilograms. What is her weight in pounds?

________ kg 2. Harold weighs 250 pounds now. If Harold goes on a diet and loses 30 pounds,

then how many kilograms will he weigh?

________ kg 3. An infant weighs 3400 grams. How much does this infant weigh in kilograms?


C. Apothecary System

The style of apothecary notations includes:

1. The unit or abbreviation typically precedes the amount. Example: gr v

2. Lowercase Roman numerals are often used to express whole numbers.

3. Fractions are used to designate amounts less than 1. Example: gr 1

2 , gr

1

4

4. Symbol ss used to designate the fraction 1

2 but, because this symbol can

easily be misinterpreted thus, it is no longer used.

Arabic Number Roman Numeral Apothecary Notation

1

l i or l

2

ll ii or ll

4

lV iv

5

V v

9

lX ix

10

X x

15

VX vx

20

XX xx

Equivalents:

gr i = 60 mg or 65 mg

Example # 1:

Convert: 120 mg to gr

Approximate equivalent: gr i = 60 mg. Conversion factor is 60 mg/gr

THINK: Smaller ↑ Larger → Divide

120 mg ÷ 60 mg/gr = gr 2 (Wrong)

gr ii (Correct)


Example # 2:

Order: phenobarbital gr ii PO q 8h.

On hand: phenobarbital 60 mg per tablet.

What is the amount to administer? (Use gr i = 60 mg)

gr ii x 60 mg

gr x

1 tab

60 mg =

2 x 60

60 = 2 tabs

_____________________________________________________________________________________

Practice Exercises:

______ gr 1. Convert 2400 mg to grains. (Use gr i = 60 mg)

_____mg 2. An order is for gr iii of medication. How many milligrams should the patient

receive? (Use gr i = 65 mg)

______ mL 3. Calculate the amount you will prepare for one dose.

Order: atropine gr 1/100 IM on call to O.R

Supply: atropine 0.4 mg/mL (Use gr i = 60mg)


______ mL 4. Order: morphine sulfate gr ¼ IM stat

Supply: morphine sulfate 10 mg/mL

How many milliliters of morphine would you administer? (Use gr i = 60 mg)

_________ 5. The physician ordered acetaminophen gr x po q6h prn for mild to moderate pain.

______tab/s

Stock available:

A. acetaminophen 325 mg tab.

B. acetaminophen 500 mg tab.

Which tablet are you going to use A or B & how many tab/s are you going to

administer? (Write your two (2) answers in the spaces provided.)


D. Other Common Drug Measurements

Four other measurements maybe used to indicate quantity of medicine prescribed:

international unit, unit, milliunit, and milliequivalent.

It is not necessary to learn conversions for these units of measure because medications

prescribed in these measurements are also prepared and administered in the same system.

Insulin and Epogen are measured in units

Potassium Chloride is measured in milliequivalent / mEq


Module V: Time____________________________________________________

Traditional Time International Time/ Military Time/

24h Clock Time

12:00 midnight or 12:00 AM

2400

1:00 AM

0100

6:00 AM

0600

11:00 AM

1100

12:00 noon or 12:00 PM

1200

1:00 PM

1300

6:00 PM

1800

11:00 PM

2300

Rules:

1. Traditional time and international time are the same hours starting with 1:00 AM or 0100

through 12:59 PM or 2359.

2. Minutes after 12:00 AM and before 1:00 AM are 0001 through 0059 in international

time.

3. Hours starting with 1:00 PM through 12:00 AM are 12:00 hours greater in international

time.

4. International time is designated by a unique four-digit number without a colon.

Example # 1:

1. 5:00 PM = 5:00 + 12:00 = 1700

2. 12:35 AM= 1235 – 1200 = 0035

3. 2000 = 2000 – 1200 = 8:00 PM

4. 0005 = 0005 + 1200 = 12:05 AM


Example # 2:

The patient receives an initial dose of medicine at 12:00 PM while in the physician's

office. The physician orders the medication to be taken every 6 hours. The patient should

be told to take the next dose at __________ (Use military time/24h clock time.)

1200 or 12:00 PM initial dose/1 st dose

+ 6 hrs for the next dose

1800

Practice Exercises:

_______1. Convert 1139 to conventional time.

Practice Exercises 2 and 3, refers to this scenario.

Scenario: A patient was prescribed metronidazole 500 mg PO q8h. The initial dose was

taken at 8:00 AM.

_______ 2. At what time will the patient take the next dose? (Use conventional time)

_______ 3. At what time will the patient take the 3rddose? (Use military time/24h clock time)


Module VI: Temperature_____________________________________________

The Fahrenheit scale establishes the freezing point of pure water at 32 degrees

and the boiling point of pure water at 212 degrees.

The Celsius scale establishes the freezing point of pure water at 0 degrees

and the boiling point of pure water at 100 degrees.

Conversion: Fahrenheit to Celsius, first subtract 32 and then divide the result by 1.8

ºC = ℉ − 32

1.8

Example:

Convert 98.6oF to degrees Celsius.

ºC = 98.6− 32

1.8

ºC = 66.6

1.8 = 37

Therefore, 98.6 ºF = 37 ºC

Practice Exercises:

_______ C 1. Convert 99.5o F to degrees Celsius.

______ C 2. Convert 97.2o F to degrees Celsius. (Round off to the second decimal

number/place.)


______ C 3. A mother brought her 6 yr old boy to the physician’s office due to fever, with

current temperature of 100.2 F which is equivalent to ____ C. (Round off to the

first decimal number/place.)

Practice Exercises 4 and 5, refers to this scenario.

Scenario: The state health department requires that certain medications be stored between 36 º F

and 41 º F. The refrigerator in the medication room has a Celsius thermometer.

______ ºC 4. What should be the minimum temperature setting for the refrigerator in Celsius?

(Round off to the second decimal place/number.)

______ ºC 5. What should be the maximum temperature setting for the refrigerator in Celsius?


Conversion: Celsius to Fahrenheit, first multiply by 1.8 and then add 32

ºF = ºC x 1.8 + 32

Example:

Convert 37 ºC to ºF

ºF = 1.8(37) + 32

ºF = 66.6 + 32

ºF = 98.6

Therefore, 37 ºC = 98.6 ºF

Practice Exercises:

______º F 1. Convert 38.6 ºC to degrees Fahrenheit. (Round off to the first decimal

number/place.)

______º F 2. Convert 40 ºC to degrees Fahrenheit.

______º F 3. Convert 39.3 ºC to degrees Fahrenheit. (Round off to the first decimal

number/place.)


Module Vll: Drug Dosage Calculations_________________________________

1. Oral Dosages

Example: The physician ordered 0.5 g of Zithromax four times daily for 3 days.

What is the amount to administer? Refer to label for dosage on hand.

Computation:

0.5 g

200 mg x

1000 mg

1 g x 5 mL = 12.5 mL

____________________________________________________________________________________

Practice Exercises:

_______ cap/s 1. The order is Tikosyn (dofetilide) 0.5 mg PO bid.

Stock on hand is Tikosyn (dofetilide) 125 mcg/cap.

Calculate how many capsule/s of this medication should be given to the patient.


_______tab/s 2. Order: Increase patient's current dose of Celexa 10 mg PO daily to 20 mg per day

starting next dose. See label below for dosage on hand. The new amount to administer

is ____________.

________________________________________________________________________________________________________

________ tab/s 3. The physician orders acyclovir 400 mg PO three times a day for herpes. The

medication is supplied in 800 mg tablets. How many tablets will the nurse

administer?


Practice Exercises 4 through 6 , refers to this label.

_______ mL 4. Ordered: EES Granules 400 mg PO q6h.

See label above for dose on hand.

The amount to administer per dose is ________.

_______ mg 5. How many milligrams does the whole bottle contain? (Read: Directions for

mixing or reconstituting the medicine.)

______ days 6. Based on the above computation, how many days will the whole bottle last?


_____ mL 7. Order: Nilstat Oral Suspension 250,000 units PO q.i.d.

Supply: Nilstat Oral Suspension 100,000 units per mL

How many milliliters of the medication would be given to the patient per day?

_______ g 8. The order reads Glucotrol (glipizide) 15 mg PO daily ac breakfast. How many

grams of this medication would you administer?

______ tab/s 9. The physician orders potassium chloride crystals CR 40 mEq twice a day orally

for a patient with hypokalemia. Potassium chloride crystals CR are available in

20 mEq tablets. How many tablets would the nurse administer with each dose?


_______ mg 10. Ordered amoxicillin/clavulanate 875 mg every 12 hours.

See label for medication on hand.

What is the amount to administer?

(Base dose on amount of amoxicillin available.)

(Round to the first decimal number.)


2. Parenteral Dosages

Example: Order: Humalog 15 units subcutaneous injection BID. Refer to label for drug on hand.

How many mL of Humalog will the patient receive?

Computation:

15 units x 1mL

100 units = 0.15 mL

____________________________________________________________________________________

Practice Exercises:

_____ mL 1. Order: Humalog 5 units subcutaneous injection every morning. (Refer to label below

for dose on hand.) How many milliliters of insulin will the patient receive?


Practice Exercises 2 and 3 refer to this scenario.

Scenario: The patient has the following order:

> Humulin N 20 units subcutaneous injection every morning.

> Regular Insulin subcutaneous injection ac & hs per sliding scale.

Blood Glucose Reading Insulin Dose per Sliding Scale

151 – 200 mg/dl = 2 units

201 – 250 mg/dl = 4 units

251 – 300 mg/dl = 6 units

301 – 350 mg/dl = 8 units

Greater than 350mg/dl = call MD

Stock on Hand: Humulin N 100 units per mL

Regular Insulin 100 units per mL

______ mL 2. The patient’s blood glucose before breakfast is 250 mg/dl. How many milliliters

of insulin will the patient receive?

______ units 3. What is the total amount of insulin the patient will receive this morning?


_______mL 4. Calculate the amount to administer per day.

Order: Heparin 2500 units subcutaneous injection bid

Supply: Heparin 20000 units per mL

_______ mL5. Calculate the amount to administer. Choose the correctly marked syringe.

_______ syringe

Ordered: Lanoxin 0.125 mg deep IM stat.

On hand: Lanoxin 0.25 mg/mL.


______ mL 6. Order: tobramycin sulfate 90 mg IM q8h

Supply: Nebcin (tobramycin sulfate) 80 mg per 2 mL

How many milliliters are you going to administer? (Round off your answer

to the first decimal number/place.)

______ mL 7. The physician orders Imferon 90 mg IM (Z track) for anemia. The medication is

supplied in 50 mg/mL. How many milliliters will the nurse administer?

(Round to the 1st decimal number if the dose is greater than 1 mL.)

______ mL 8.The physician orders Methergine 0.3 mg IM for postpartum bleeding.

The medication is supplied in 0.2 mg/mL.

How many milliliters will the nurse administer?

Shade the syringe.


______ mL 9. The physician orders furosemide 60 mg IV push stat for edema. How many

milliliters will the nurse administer?

(Round to the 1st decimal number if the answer is greater than 1 mL.)

______10. A patient with renal failure has orders for Epogen 5000 units subcutaneous every

Monday, Wednesday, and Friday; hold if hemoglobin is greater than 11 g/dL. The

Epogen is supplied in 10000 units per 1 milliliter vials. How many milliliters would

the nurse administer?


C. Dosages Based on Body Weight

Rule:

1. Convert the weight from pounds to kilograms (rounded to the 1st decimal number).

2. Calculate the dosage in milligram per kilogram. Multiply mg by weight in kg.

3. Compare the ordered dosage to the recommended dosage, and decide if the dosage is safe.

Example: The physician orders palifermin (Kepivance) 60 mcg/kg body weight to be

administered daily. The client weighs 88 lb. The medication is supplied 5 mg/ml.

How many milliliters would you administer per dose?

Computation:

88 lb ÷ 2.2 = 40 kg

60 mcg

kg x

1 mg

1000 mcg x 40 kg x

1 mL

5 mg =

60 x 1 x 40 x 1

1000 x 5 mL =

2400

5000 mL = 0.48 mL

_____________________________________________________________________________________

Practice Exercises:

______ mL 1. The physician orders oxacillin sodium 200 mg/kg body weight per day. The

client weighs 66 pounds. The medication is supplied 500 mg/ml. How many

milliliters would you administer?


Practice Exercises 2 through 5, refers to this scenario.

_______ mg 2. What is the recommended minimum single dosage for this child? (Round off

to the second decimal number/place.)

______ mL 3. How many milliliters of the minimum single dose will you give this child?

_______ mg 4. What is the recommended maximum single dosage for this child? (Round off

to the first decimal number.)

_______ mL 5. How many milliliters of the maximum dose will you give this child

per day?

Scenario: Order: furosemide oral solution 10 mg po b.i.d. for a child who weighs 16 lbs.

The recommended pediatric dosage is 0.5 – 2 mg/kg to be given in two divided doses.

The label reads: furosemide 10 mg/mL oral solution.

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Math and Dosage Calculations Module