Units of Measurement and Conversions
Course
Practicum in
Health SciencePharmacology
Rationale
Basic math principles are important in providing quality client care when
pharmaceuticals are involved and knowledge of various measurement
systems is essential in proper dosage calculation for client safety.
Unit VII
Career
Preparation and
Employability
Objectives
Upon completion of this lesson, the student will be able to:
 Know the measurement systems associated with pharmacology
 Perform the mathematical processes related to pharmacology
 Apply concepts of measurement functions in multiple-step conversion
problems
 Convert between measurement systems to calculate drug dosages
Essential
Question
Why is having a
good math skill
important in the
Health care
field?
Engage
A physician orders a medication that is given according to a patient’s weight.
Give 1mg/kg to your patient. Your patient weighs 154 lbs.
How much does he weigh in kg, and how much medication will you give.
TEKS
130.205(c)
1A, 2A, 2B, 7A
Key Points
I. The apothecary system – based on 12-ounce pound
A. Officially replaced by metric system
B. Standard unit of measure for weight (solid substances) is the grain
(gr)
Prior Student
Learning
Basic math skills
Estimated time
3 - 5 hours
C. Liquid volumes (fluids) are measured by minim
D. Rarely used today
II.
Common household system
A. Less accurate system of measurement
B. Primarily used by patients who take medication at home
C. Practitioner’s responsibility to assure consumer is taking correct dose
D. Necessary for practitioner to know equivalents from “pharmacy
language” to every day common household terms
E. Conversions
1. Standard teaspoon established to contain approximately 5 ml
2. 60 gtt. (gtt. = drops) = 1 teaspoonful
3. 3 teaspoons = 1 tablespoon
4. 1 teaspoon = approximately 5 Gm or g (gram)
5. 1 teaspoon = approximately 60 gr (gr = grain; not to be
confused with g = gram)
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III. Metric system – most commonly used system in measurement, easy to
use since based on parts and multiples of 10
A. Official system of measure for pharmacy practice
B. Advantages
1. simple
2. brief
3. adaptable
4. universal
C. Metric measures for
1. length
2. area
3. volume
4. weight
5. temperature
D. Pharmacy mainly concerned with weights and volumes of drugs
E. Decimal system that can be divided into any parts that are multiple of
10 (10, 100, 1000, etc.)
F. Greek and Latin prefixes indicate what multiple is used, e.g. milli-,
centi-, deci-, micro-, kilo-, etc.
G. Standard unit of metric measure for capacity or volume is liter
H. Standard unit of measure for weight is gram
I. May encounter physician’s orders or prescriptions requiring
conversion
1. Within same system (e.g., convert 0.350 Gm to 350 mg –
quantities both metric but using milligrams may be more
convenient)
2. From one system to another (e.g., 170 pounds to 77 kilograms
because most drugs dosage requirements are determined by
body weight in kg)
3. Translation from one system to another or within the same
system is called conversion
4. Most physicians not cognizant of the various existing systems and
may write orders that appear to be jumbled quantities
J. Liquid drug preparations
1. Creams and ointments are expressed as percentage
concentrations
2. A certain quantity of the drug is contained in the final quantity of
the product
a. 1 % hydrocortisone cream contains 1 g of hydrocortisone in
100 g final product (the actual drug plus the cream)
b. 5% sodium chloride solution contains 5 g sodium chloride in
100 ml final product ( NaCl and distilled water)
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c. 1 gram in 100 grams or 1/100 equal to 0.01, or 1%
d. 5 grams in 100 milliliters equal to 5/100 or 0.05, or 5%
Activity
I.
Complete Practice Problems
II.
Complete Unit Equivalency Practice
III.
Complete Dosage Calculations
IV. Review actual prescriptions, physician’s hospital orders, and /or bulk
drug manufacturing requests that require decimals, ratio/proportion,
and percentage calculations. Discuss, in small groups, the various
systems used for drug calculations, determining preferences and
justifying why.
V.
Complete the Salt Hand and Foot Scrub Activity
Assessment
Successful completion calculation problems
Materials
Practice problem handouts
Actual prescriptions and/or physician’s orders for medications (can be
obtained from your physician or copies from hospital charts as long as
information identifying patient and institution have been sufficiently
obliterated – check with hospital administration if needed!)
Conversion charts
Salt Hand and Foot Scrub Activity
 Epsom Salts, Baking Soda or Brown Sugar, Salt / Sea Salt, vegetable
oil, and essential oils / food flavoring oils
 Parchment paper or copier paper cut in appropriate size for students
to collect each ingredient
 1 or 2 digital scales to weigh
 Household measuring cups and spoons – enough for stations
 Plastic or glass containers large enough to hold enough ingredients
for a class period
 Disposable foam or other type of bowls
 Disposable spoons
 Glass mortars & pestles -- enough for groups or stations
 Containers – individual 1 cup containers or old baby food jars with lids
 Label
 Curling ribbon
 Optional -- disposable plastic ice cream spoons or baby food spoons
– for scooping scrub
Copyright © Texas Education Agency, 2013. All rights reserved.
Accommodations for Learning Differences
For reinforcement, the student will review math conversation and complete
the coherent sequence pretest.
For enrichment, the student will develop health care related word and
conversion problems directed to middle school mathematics. Include
teaching aids to reinforce the relationship between measurements.
National and State Education Standards
National Healthcare Foundation Standards and Accountability Criteria
Foundation Standard 1: Academic Foundation
Healthcare professionals will know the academic subject matter required for
proficiency within their area. They will use this knowledge as needed in their
role. The following accountability criteria are considered essential for
students in a health science program of study.
1.3 Medical Mathematics
1.31 Apply mathematical computations related to healthcare procedures
(metric and household, conversions and measurements).
1.32 Analyze diagrams, charts, graphs, and tables to interpret healthcare
results.
1.33 Record time using the 24-hour clock.
TEKS
§130.205 (C)(1)(A) interpret data from various sources in formulating
conclusions;
§130.205 (C)(2)(A) accurately describe and report information, according to
facility policy, observations, and procedures;
§130.205 (C)(2)(B) demonstrate therapeutic communication skills to provide
quality care; and
§130.205 (C)(7)(A) interpret knowledge and skills that are transferable
among health science professions;
College and Career Readiness Standards
Mathematics Reasoning
A. Expressions and equations
1. Explain and differentiate between expressions and equations using words
such as “solve,” “evaluate,” and “simplify.”
B. Manipulating expressions
1. Recognize and use algebraic (field) properties, concepts, procedures, and
algorithms to combine, transform, and evaluate expressions (e.g.,
polynomials, radicals, rational expressions).
C. Solving equations, inequalities, and systems of equations
1. Recognize and use algebraic (field) properties, concepts, procedures, and
algorithms to solve equations, inequalities, and systems of linear equations.
IV. Measurement Reasoning
Copyright © Texas Education Agency, 2013. All rights reserved.
B. Systems of measurement
1. Convert from one measurement system to another.
2. Convert within a single measurement system.
VIII. Problem Solving and Reasoning
A. Mathematical problem solving
1. Analyze given information.
2. Formulate a plan or strategy.
3. Determine a solution.
Cross Disciplinary Standards
I. Key Cognitive Skills
E. Work habits
1. Work independently.
2. Work collaboratively.
Copyright © Texas Education Agency, 2013. All rights reserved.
MATHEMATICS CONVERSION CHART
Length
1 meter = 100 centimeters
1 meter = 1000 millimeters
10 millimeters = 1 centimeter
1 inch = 2.5 centimeters
Volume for Fluids
1 liter = 1000 milliliters
1 milliliter = 1 cubic centimeter
10 centiliters = 1 deciliter
10 deciliters = 1 liter
1 teaspoon = 5 milliliters
1 tablespoon = 15 milliliters
1 ounce = 30 milliliters
1 pint = 500 milliliters
1 quart = 1000 milliliters
Weight Conversions
1 gram = 1000 milligrams
1 kilogram = 1000 grams
1 kilogram = 2.2 pounds
1 pound = 16 ounces
Temperature Conversions
Celsius to Fahrenheit (0C x 1.8) + 32 = 0F
Fahrenheit to Celsius (0F – 32) ÷ 1.8 = 0C
Terms and abbreviations
Gram (g) measures mass or weight
Liter (l) measures volume or liquid
Meter (m) measures length or distance
Kilo (k) = thousands
Deci (d) = tenths
Centi (c) = hundredths
Milli (m) = thousandths
Copyright © Texas Education Agency, 2013. All rights reserved.
DOSE AND DOSAGES
YOUNG'S RULE:
Child's Dose = (Child's Age (in years)/Child's Age in Years + 12) x Adult Dose
FRIED'S RULE:
Infant's Dose = (Age (in months) /150 pounds) x Adult Dose
CLARK'S RULE:
Child's Dose = (Weight of Child (in pounds) / 150 pounds) x Adult Dose
Child's Dose = (Weight of Child (in kilograms) / 68 kilograms) x Adult Dose
SOLUTIONS
Ratio Strength of Solutions = amount of drug / amount of solution
Percent of Strength by Volume = (volume of solute/volume of solution)x100
Percent Strength by Weight (Mass) = (mass of solute/volume of solution)x100
Amount of Solute /Amount of First Solution = Amount of Solute / Amount of Second Solution
BODY SURFACE AREA
Used to determine drug dosage in infants and children and also used to determine the loss of
body fluid in ml/hour in burn patients.
Formula: BSA (m2)=0.20247 x height (m) 0.725 x weight (kg)0.425
Web site to automatically calculate BSA:
http://www-users.med.cornell.edu/~spon/picu/calc/bsacalc.htm
http://www.halls.md/body-surface-area/bsa.htm
IV DROP RATE CALCULATION
CC’S/hour x Drop Factor of the tubing divided by 60 (minutes) = drops/minute
Copyright © Texas Education Agency, 2013. All rights reserved.
DOSAGE CALCULATIONS
EXAMPLE: Scenario: The patient is to receive 1L of Lactated Ringer’s solution continuous
IV q8hr. The primary administration set delivers 15 gtts/ml. At the beginning of the shift the
1L bag is found to contain 250 ml. When checking the drip rate you find the infusion to be
running at 30 gtts/min. When will the next bag be due to be hung?
This problem needs to be worked in two separate steps – the first one is to determine the
rate required to infuse the ordered dose over the time specified. Remember that the scenario
only states what you found – you always have to double check for yourself to ascertain
accuracy! Whoever started this IV before your shift may have calculated incorrectly and if
you do not correct the rate you will be responsible for any undesirable results as well!
1. Find the pertinent solution required to solve the problem in the above scenario and
mentally eliminate the rest.
Pertinent information: 1 L/8 hrs (one entire dose); 15 gtt/ml; 30 gtt/min; 250 ml/dose
(remainder from whole dose)
2. Determine what unit equivalency conversions you need.
Unit equivalency conversion: 1000 ml/L; 60 min/hr
3. Determine the desired units; what is the problem asking for?
Desired units: (1) gtt/min; (2) time in hr and/or min
Copyright © Texas Education Agency, 2013. All rights reserved.
PRACTICE PROBLEMS
Solve the following problems:
1. How many cc in ½ tsp?
2. Convert 20 gtt to cc
3. How many qt in 4 fl oz?
4. Convert 1.5 inches to cm
5. Convert 0.05 g to µg
6. Convert 0.0025 L to cc
7. Convert 0.25 g to gr
8. Convert 1/40 gr to mg
9. How many tsp in 2 Tbs?
10. Convert 88 lb to kg
Solve the following problems by making sure you list all the available information provided,
extract the conversion factors from the information provided, and set up the conversion factors
for the cancellation of the unwanted units.
1. Ordered: Furosemide 40 mg p.o.
Available: Furosemide 20 mg tablets
Calculate the number of tablets per dose
2. Ordered: Tylenol 500 mg p.o. stat.
Available: acetaminophen 500 mg tablets
Calculate the number of tablets per dose
3. Ordered: Premarin 1.25 mg PO
Available: conjugated estrogens 0.625 mg tablets
Calculate the number of tablets per dose
4. Ordered Procardia XL 60 mg b.i.d.
Available: Procardia XL 30 mg capsules
Calculate the number of capsules per dose
5. Ordered: Biaxin 500 mg po bid
Available: Biaxin 250 mg tablets
Calculate the number per dose
Copyright © Texas Education Agency, 2013. All rights reserved.
6. Ordered: diphenhydramine 25 mg IM now
Available: Benadryl 50 mg/ml in 10 ml vial
Calculate the number of ml/dose
7. Ordered: Epinephrine 0.3 mg SQ stat
Available: Epinephrine 1 mg/ml in 5 ml vial
Calculate the number of ml per dose
8. Ordered: Fer-In-Sol 5 mg PO qd
Available: Fer-In-Sol 15 mg/0.6 cc
Calculate the number of ml for a 90 d supply.
9. Ordered: Phenobarbital ¼ gr PO qid
Available: Phenobarbital 15 mg tablets
Calculate the number of tablets/dose.
10. Ordered: Rocephin 1 g in 100 ml D5W IV b.i.d.
Available: Rocephin sterile crystalline 250 mg/vial
Calculate the number of vials per dose.
Copyright © Texas Education Agency, 2013. All rights reserved.
Answer Key: Practice Problems
1. 2.5 cc
2. 1.3 cc
3. 0.125 qt
4. 3.81 cm
5. 50,000 µg
6. 2.5 cc
7. 4.17 gr
8. 1.5 mg
9. 6 tsp
10. 40 kg
Dosage Problems:
1. 40 mg/dose; 20 mg/tab; 40mg; 20 mg  2 tab/dose
dose tab
2. 500 mg/dose; 500 mg/tab; 500 mg; 500 mg  1 tab/dose
dose
tab
3. 1.25 mg/dose; 0.625 mg/tab; 1.25 mg; 0.625mg  2 tab/dose
dose
tab
4. 60 mg/dose; 30 mg/cap; 2 dose/d; 60 mg; 30 mg  2 cap/dose
dose
cap
5. 500 mg/dose; 250 mg/tab; 2 dose/d; 500 mg; 250 mg  2 tab/dose
dose
tab
6. 25 mg/dose; 50 mg/ml; 10 ml/vial; 25 mg; 50 mg  ½ ml/dose
dose ml
7. 0.3 mg/dose; 1 mg/ml; 5 ml/vial; 0.3 mg; 1 mg  0.3 ml/dose
dose ml
8. 5 mg/dose; 15 mg/0.6 cc; 1 dose/d; 90 d; 5 mg ; 15 mg  18 cc
dose 0.6 ml
9. ¼ gr/dose; 15 mg tab; 4dose/d; 60 mg/gr (unit equivalence);
1 gr; 15 mg; 60 mg;  1 tab/dose
4
tab
gr
10. 1 g/dose; 1 g/100 ml; 250 ml/vial; 2 dose/d; 1000 mg/g (unit equivalence);
1 g; 250 mg; 1000 mg  4 vial/dose
dose vial
1g
Copyright © Texas Education Agency, 2013. All rights reserved.
UNIT EQUIVALENCY PRACTICE
Convert the following units
1. 1 g to mg
2. 5 mg to µg
3. 0.0025 L to ml
4. 10 gr to mg
5. 68 lb to kg
6. 15 cc to tsp
7. 500 cc to L
8. 36.8o C to o F
9. 15 ml to Tbs
10. 120 µgtt to cc
11. 15 ml to gtt
12. 1 fl oz to ml
13. 2 gr to g
14. 25 cc to ml
15. 1 tsp to cc
16. 10 km to ft
17. 180 lb to kg
18. 0.0005 mg to µg
19. 500 µg to kg
20. 98.6o F to Celsius
21. 25 gr to mg
22. 1 hr to min
23. 20 kg to lb
24. 1 pt to fl oz
25. 15 gtt to µgtt
26. 1 pt to ml
Copyright © Texas Education Agency, 2013. All rights reserved.
ANSWER KEY TO UNIT EQUIVALENCY
1. 1 g = 1000 mg  1000 mg
2. 1 mg = 1000µg  5000 µg
3. 1000 ml = 1 L  2.5 ml
4. 60 mg = 1 gr  600 mg
5. 2.2 lb = 1 kg  30.9 kg
6. 5 cc = 1 tsp  3 tsp
7. 1000 ml = 1 L, 1 cc = 1 ml  0.5 L
8. 98.2o F
9. 5 ml = 1 tsp, 3 tsp = 1 Tbs  1 Tbs
10. 1 ml = 60 µgtt  2 cc
11. 1 ml = 15 gtt  225 gtt
12. 1 fl oz = 30 ml  30 ml
13. 1 gr = 60 mg, 1000 mg = 1 g  0.12 g
14. 1 cc = 1 ml  25 ml
15. 5 cc = 1 tsp  5 cc
16. 2.54 cm = 1 in, 12 in = 1 ft  32,808.4 ft
17. 2.2 lb = 1 kg  81.82 kg
18. 1000 µg = 1mg  0.5 µg
19. 1,000, 000 µg = 1 kg  0.0005 kg
20. 37o C
21. 60 mg = 1 gr  1500 mg
22. 60 min = 1 hr  60 min
23. 2.2 lb = 1 kg  44 lb
24. 16 fl oz = 1 pt  16 fl oz
25. 1 ml = 15 gtt, 1 ml = 60 µgtt  60 µgtt
26. 1 pt = 16 fl oz, 30 cc = 1 fl oz  480 ml
Copyright © Texas Education Agency, 2013. All rights reserved.
SALT HAND AND FOOT ACTIVITY – STUDENT HANDOUT
1/8 cup MgSO4
1/8 cup NaHCO3 or C12H22O11
1/8 cup NaCl
1 tablespoon C54H100O7
10 gtts essential oil or food flavoring oils
** coloring (optional)
Zero the scale and weight your parchment paper. ______________ wt
Zero scale with parchment paper and measure out your Salts:
MgSO4
__________
NaHCO3
__________ or C12H22O11 __________
NaCl
__________
Pour MgSO4 salts into a glass mortar use pestle to break down clumps and salt. Once the
MgSO4 has been broken down into smaller size, place in a bowl and mix in the other
ingredients and add the C54H100O7. Make sure all ingredients are well blended.
Add five drops of an essential oil scent that you enjoy and blend it in well, then add five more
drops and continue to blend.
**Color optional – add 2 drops at a time to get desired shade
Package your scrub in an airtight container and label.
Create a Label with the following instructions and list the common name for the
ingredients. Give your scrub a name.
Instructions -- Rub scrub into hands or feet for 2 - 5 minutes. Rinse and wash with your favorite
hand soap.
Follow with your favorite lotion
Copyright © Texas Education Agency, 2013. All rights reserved.
Salt Hand and Foot Scrub Activity -- Teacher Information
Materials Needed
 Epsom Salts, Baking Soda or Brown Sugar, Salt / Sea Salt, vegetable oil, and essential
oils / food flavoring oils
 Parchment paper or copier paper cut in appropriate size for students to collect each
ingredient
 1 or 2 digital scales to weigh ingredients (may be borrowed from a science teacher or if
not available you do not need to have students weigh the ingredients)
 Household measuring cups and spoons – enough for stations
 Plastic or glass containers large enough to hold enough ingredients for a class period
 Student Handout copies
 Disposable foam or other type of bowls
 Disposable spoons (students will use to mix ingredients)
 Glass mortars & pestles enough for groups or stations
 Containers – individual 1 cup containers or old baby food jars with lids (adjust amounts of
salts/ingredients depending on container size)
 Label – students can create label on an index card or with computer to print
 Curling ribbon – students can attach their label and decorate their final product
 Optional -- Disposable plastic ice cream spoons or baby food spoons – for scooping
scrub
Put the ingredients in plastic or glass containers with the chemical names to be used in stations.
You can have students in pairs or individuals – have them look up the common names on the
internet.
1/8 cup Epsom Salts/ MgSO4
1/8 cup Baking Soda /NaHCO3 or Brown Sugar/ C12H22O11
1 tablespoon Salt or Sea Salt / NaCl
¼ cup Vegetable Oil / C54H100O7
10 gtts essential oil – must be safe to use on skin or you may use food flavoring oils (e.g.,
strawberry, coconut, banana, etc.) – must be safe to use on skin
** coloring (optional) – If you use baking soda you will be able to color the scrub. If using Brown
Sugar the color will not take.
Copyright © Texas Education Agency, 2013. All rights reserved.
Below are the chemical names you can print to place with your ingredients.
MgSO4
NaHCO3
NaCl
C12H22O11
C54H100O7
Copyright © Texas Education Agency, 2013. All rights reserved.