MATH14310
Mathematics for Nurses
Module2
Week3 Lecture1
Systems of Measurements
Yue Xin Lei RN, BScN, MN
Spring/Summer 2022
Learning Objectives
1. Identify metric units.
2. Accurately express metric units commonly used in the health sector.
3. Accurately interpret the relationship between selected metric prefixes.
4. Recognize common equivalents between the metric and the household
systems.
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-2
Learning Objectives
5. Identify and accurately express non-metric units used in the health sector.
6. Convert within and between the metric and household systems.
7. Convert between traditional and international time.
8. Convert between temperature scales.
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-3
Measurement Systems
Systems used in Canada:
1. International System of Units (SI) or the Metric System
2. Apothecaries System of Measurement
3. Household System of Measurement
Healthcare professionals are expected to understand and know how
to convert among these systems
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
The Metric System
(International System of Units (SI Units))
• Up-to-date version of metric system
• Advantages:
 Coherent
 Logical
 Simple to use
• 98% of the world uses this system. Enhances global communication via
uniform descriptions, terms, and symbols.
Example: number + unit 1g, 10m, 1kg, 50s
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
SI Units Used in the
Health Sector
Adapted from Dosage Calculations, 4th edition by Nelson Education Ltd.
SI Units Used in the Health Sector
Common SI (Metric)
Abbreviations
SI (Metric) Units Conversions/
Conversion Factor
gram = g
microgram = mcg
milligram = mg
kilogram = kg
liter = L
milliliter = mL
meter = m
Centimeter =cm
millimeter = mm
Weight
1 kilogram (kg) = 1 000 grams (g)
1 gram (g) = 1 000 milligrams (mg)
1 milligram (mg) = 1 000 micrograms (mcg)
Volume
1 litre (L) = 1 000 milliliters (mL)
1 milliliter (mL) = 0.001 litre (L)
Length
1 meter (m) = 100 centimeters (cm) = 1 000 mm
1 millimeter (mm) = 0.001 meter (m) = 0.1 cm
Adapted from Dosage Calculations, 4th edition by Nelson Education Ltd.
Common Use
Measuring body
weight
Parenteral and oral
medications
Pediatric medication
IV solution orders
Parenteral and oral
medications
Measuring body
height
Common Prefixes Used in Health Care
Prefix
Kilo*
Numerical
Value
1 000
Meaning
one thousand times
Hecto
100
one hundred times
Deka
Deci
Centi*
10
0.1
0.01
ten times
one tenth
one hundredth part of
Milli*
0.001
one thousandth part of
Micro*
0.000 001
one millionth part of
*Prefixes used most often in medication administration.
Adapted from Dosage Calculations, 4th edition by Nelson Education Ltd.
Rules for Metric Notations
1. Unit must always follow amount
– 5g
2. No period after unit abbreviation
– 20 mg
3. No “s” to make a unit plural
– 5 mL
4. Add space between amount, unit
– 20 mg
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-9
Rules for Metric Notations
5. Add space for amounts larger than
4 digits, no commas
– 10 000 units
6. Use decimals for fractional amounts
– 1.5 mL
7. Add leading zero for amounts less than 1
– 0.5 mg
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-10
Rules for Metric Notations
8. Remove trailing zeros
–
1.5 mg
9. Do not use 𝜇g – use mcg instead
–
61 mcg
10. Do not use cc – use mL instead
–
400 mL
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-11
Household System of Measurement
• Non-metric units are used in the community for some
measurements
• Important to convert patient report to metric units
• Example:
– 1 tsp is approximately 5 mL
– 1 cup is approximately 8 oz/240 mL
– 2.2 lb is approximately 1 kg
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-12
Apothecary System of Measurement
• First system used by pharmacists, physicians, uses Roman
numerals instead of digits
• Some orders may include this
• Example:
– Tylenol #3 i-ii tabs PO q 4-6h prn
• Always consult prescriber if in doubt
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-13
Special Classes of Units of Measurement
• Some measurements used to indicate strength/potency of a
drug are unique
• Can’t be converted into other systems
• Units, International Units (IU)
– Common in insulin, hormones, vitamins, penicillin,
anticoagulants
• Units millimoles (mmol), milliequivalents (mEq)
– Seen in potassium chloride
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
3-14
Converting Within the International System
of Units or Metric System (SI)
• Nurses often make conversions within the metric system when
administering medications. E.g. from grams to milligrams
• To make conversions within the metric system, remember the
common conversion factors or its unit equivalent (Eg. 1 kg =1000 g,
1 g =1000 mg, 1 mg =1000 mcg etc.)
Converting Within the Metric System (SI)
Rule 1: To convert a smaller unit to a larger one, divide by
moving the decimal point three places to the left.
Example: 100 mL = _______ L
(smaller) (larger)
(conversion factor: 1000 mL = 1 L)
100 mL = .100 = 0.1 L (Placing zero in front of the decimal is important)
or
100 ÷ 1000 = 0.1 Thus, 100 mL = 0.1 L
Rule 2: To convert a larger unit to a smaller one, multiply by
moving the decimal three places to the right.
Example: 0.45 kg = ______ g
(larger) (smaller)
(conversion factor: 1 kg = 1000 g)
0.45 kg = 0.450 = 450 g or 0.45 x 1000 = 450
Thus, 0.45 kg = 450 g
Commonly Used Non-SI Units
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
Apothecary System
• It is the first system of medication measurement
• Notations in this system are considered confusing
• It uses Roman numeral system (refer to textbook or posted file on Roman
numerals)
Apothecary Units Abbreviations Conversion Factors
Common Use
grain
gr
1 gr = 60 mg
Some solid oral
medications like aspirin
dram
dr
1 dr = 4 or 5 mL = 60 minims
Cough medicine
ounce or fluid ounce
oz
1 oz = 30 mL = 8 dr
Antacids
quart
qt
1 qt = 1000 mL = 32 oz = 2 pt
pint
pt
1 pt = 500 mL = 16 oz
minim
D
1 minim = 1 drop = 1 gtt
15 minims = 1 mL= 15gtt
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.
Calibration on syringes
for small dose
parenteral medications
Apothecary System
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Household System
•
•
•
•
•
It is an old system and the least accurate system for measurement
Designed for everyday use at home
Has approximate equivalents (use cups, spoons & drops)
Many of the household measures originated from Apothecary system.
The increase of nursing care provided at home demands nurses to know
how to convert from one system to another
Household/Metric Equivalents
Unit
Abbreviations
Equivalent
Metric Equivalent
teaspoon
t (tsp)
—
5 mL
tablespoon
T (tbsp)
1T=3t
15 mL
ounce (fluid)
oz
1 oz = 2 T
30 mL
C
1 C = 8 oz
240 mL
lb
1 lb = 16 oz
2.2 lb = 1 kg (1 000 g)
cup (standard
measuring)
pound (weight)
Adapted from Dosage Calculations, 5th edition by Nelson Education Ltd.