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Math for the Pharmacy Technician:
Concepts and Calculations
Egler • Booth
Chapter 3: Systems of
Measurement and Weight
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3-2
Systems of Weights and Measures
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3-3
Learning Objectives
When you have successfully completed Chapter 3, you will
have mastered skills to be able to:
 Summarize metric notation.
 Calculate equivalent measurements within
the metric system.
 Identify the most frequently used equivalent
measurements among metric, household, and
apothecaries’ measurements.
 Convert measurements between the metric,
household, and apothecary systems of
measurement.
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Learning Objectives
(con’t)
 List the fundamental units of the metric
system for length, weight, and volume.
 Recognize the symbols for dram, ounce, grain,
and drop.
 Calculate temperature and time conversions.
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Introduction
 Large numbers of medications are
measured in grams and milligrams
(units of the metric system).
 Understanding and converting
systems of weights and measures are
required of pharmacy technicians.
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Metric System
 Widely used system of measurement
in the world today.
 Defined in 1792, gets its name from
the meter (basic unit of length).
 A meter is about three inches longer
than a yard.
 See next slide for Table 3-1 “Basic
Units of Metric Measurement.”
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Table 3-1 Basic Units of Metric
Measurement
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Metric System
(con’t)
 Meter and gram are abbreviated with
lowercase letters.
 Liter is abbreviated with an uppercase
L.
 This minimizes the chance of
confusion between 1 and the
lowercase L.
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Metric System
(con’t)
 Length used for measurement such
as patient height.
 Weight and volume are used to
calculate medications dosages.
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Understanding Metric
Notation
 Metric system is based on multiples of 10.
 Prefix before the basic unit indicates size.
 Kilo – indicates you multiply the basic unit
by 1000.
 Kilometer – 1000 meters
 Kilogram – 1000 grams
 Kiloliter – 1000 liters
 When you divide a meter by 1000 equal
lengths, each length is one millimeter.
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Understanding Metric
Notation (con’t)
 Prefix milli- means one-thousandth.
 Millimeter is one-thousandth of a
meter.
 Milliliter is one-thousandth of a liter.
 Milligram is one-thousandth of a
gram.
 See Tables 3-2 and 3-3 in your
textbook to visualize these concepts.
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Metric System Terms




Gram – measure unit of weight
Liter – unit of volume
Meter – unit of length
Centi- indicates 1 of the basic unit
100
 Kilo – prefix indicates basic unit times 1000
1
 Micro – indicates
of basic unit
1,000,000
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Basic Units of Metric
Measurement
Type of
Measure
Basic Unit
Abbreviation
Length
meter
m
Weight (or
Mass)
gram
g
Volume
liter
L
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Common Metric System
Prefixes
Prefix
Length
Value
kilo- (k)
kilometer
(km)
1 km = 1000 m
(basic unit)
meter (m)
1m
centi- (c)
centimeter
(cm)
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1 cm = 1 m
100
= 0.01 m
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Common Metric System
Prefixes (con’t)
Prefix
Length
Value
milli- (m)
millimeter
(mm)
1 mm = 1 m
1000
0.001 m
micro- (mc
or μ )
micrometer
(mcm)
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1 mcm =
1
m
= 1,000,000
= 0.000001
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3-16
Combining Prefixes and Units
(con’t)
Prefix
Length
(meter)
kilo-(x1000)
kilometer
km
kilogram
kg
kiloliter
kL
centi-(100)
centimeter
cm
centigram
cg
centiliter
cL
milli-(1000)
millimeter
mm
milligram
mg
milliliter
mL
micro( 1,000,000)
micrometer
mcm
microgram mcg
microliter
mcL
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Weight (Mass) Volume (liter)
(gram)
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Understanding Metric
Notation
Use Arabic numerals, with decimals to
represent any fractions.
 For example: Write 1.25 g to represent 1 1/4 g
If the quantity is less than 1, include a 0 before
the decimal point. Delete any other zeros that
are not necessary.
 For example: Do not write .750; write 0.75,
adding a zero before the decimal point and
deleting the unnecessary zero at the end.
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Understanding Metric
Notation (con’t)
Write the unit after the quantity with
a space between them.
 For example: Write 30 mg, not mg 30.
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Understanding Metric
Notation (con’t)
Use lowercase letters for metric
abbreviations. However, use
uppercase L to represent liter.
 For example: Write mg, not M.
 For example: Write mL, not ml.
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Review and Practice
 Determine the correct metric notation
for six and two-eighths milliliters.
a.
b.
c.
d.
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6.28mL
ml 6.25
1
6 4 mL
6.25 mL
Answer d. 6.25 mL
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3-21
Converting within the
Metric System
To convert a quantity from one unit
of metric measurement to
another:
1. Move the decimal point to the right if you
are converting from a larger unit to a
smaller unit.
2. Move the decimal point to the left if you
are converting from a smaller unit to a
larger unit.
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Review and Practice
1. Convert 4 L to mL.
4 L = 4.000 L = 4000 mL
2. How many m are in 75 mm?
75 mm = 75.0 mm = 0.075 m
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CAUTION
 Remember: The larger the unit, the
smaller the quantity. The smaller the
unit, the larger the quantity.
 For example: 1 dollar bill = 4 quarters = 100
pennies
 For example: 100 pennies = 4 quarters = 1
dollar bill
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Apothecary System
 An old system of measurement
 First used by apothecaries (early
pharmacists) and moved from Europe
to colonial America.
 Household system evolved from the
apothecary system.
 Very few medications are still
measured in apothecary units.
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Apothecary System Terms
 Dram ( ) – common unit of volume
in the apothecary
 Grain – basic unit
 Minim ( ) – common unit of volume
 Ounce ( ) – fluid ounces of volume
 Unit (USP Unit) – amount of
medication to produce an effect
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Apothecary System
The basic unit of weight is the grain (gr).
CAUTION!
Do not confuse grains and grams.
 grains (gr)
 grams (g)
 1 gr = 60 mg = 0.06 g OR
 1 gr = 65 mg = 0.065 g
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Apothecary System
(con’t)
The three common units of volume are
minim (
)
dram (
)
ounce (
)

CAUTION!
 Do not confuse the symbols for drams and
ounces.
 1 ounce (
) = 8 drams (
)
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Apothecary System
 Apothecary ounce is used in the
United States.
 8 ounces to a cup is commonly used
in the home to measure liquids.
 The dram
is most frequently
used to abbreviate teaspoonful which
is nearly the same volume.
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Apothecary Notation
When writing a value in the apothecary
system:
1. If a value is less than 1, write it as a
fraction. However, if the value is
one-half, write it as the
abbreviation ss.
2. Write the values with lowercase
Roman numerals.
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Apothecary Notation (cont.)
3. Use the abbreviation gr to
represent grain. Use the symbols
( ), ( ), and ( ) to represent
minim, dram, and ounce.
4. Write the abbreviation, symbol or
unit before the quantity.
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Review and Practice
1. Write four grains using apothecary
notation.
gr iv or gr iv
2. Write two and one-half grains using
apothecary notation.
gr iiss
3. Write twelve ounces using apothecary
xii
notation.
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Apothecary and Household
Equivalents
 Units of measurement found in the
apothecary and the household
systems are equal
 Apothecary ounces = household
ounces
 Neither system is based on multiples
of 10
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Abbreviations for Household
Measures
Unit of
Measurement
Abbreviations
drop
gt or gtt (plural)
teaspoon
tsp or t
tablespoon
tbs or T
ounce
oz or
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Abbreviations for Household
Measures (con’t)
Unit of
Measurement
Abbreviation
cup
cup (c)
pint
pt
quart
qt
gallon
gal
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Review and Practice
Write the quantity in Arabic numerals
before the abbreviation for the unit.
 Example: Write six drops using
household notation.
 6 gtt
 Example: Write twelve ounces using
household notation.
 12 oz
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Apothecary and Household
Equivalent Measures
drop
1 drop
=
1 minim
teaspoon
1 teaspoon
=
60 drops
tablespoon
1 tablespoon
=
3 teaspoons
ounce
1 ounce
=
2
tablespoons
cup
1 cup
=
8 ounces
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Review and Practice
How many teaspoons of solution are
contained in 1 ounce of solution?
1 oz = 2 x 1 tbs = 2 x 3 tsp = 6 tsp
How many tablespoons are in ½ cup?
½ cup = ½ x 1 cup = ½ x 8 oz = 4 oz
= 4 x 1 oz = 4 x 2 tbs = 8 tbs
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Milliequivalents and Units
 Milliequivalents (mEq)
1
1000
 The mEq is defined as
of an
equivalent weight of a chemical.
 Sodium and potassium are often
measured in mEq.
USP Units (U)
Medications such as insulin, heparin,
and penicillin are measured in units (U).
Size of the unit varies for each drug.
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Converting Among Metric,
Apothecary, and Household Systems
 When calculating drug dosages, you
must often convert among the metric,
apothecary, and household systems.
 You need to know how the measure
of a quantity in one system compares
to its measure in another system.
1 tsp = 5 mL = 5 cc
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Equivalent Volume
Measurements
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Metric
Household
Apothecary
5 mL
1 tsp
1 dr
15 mL
1 tbs
3 or 4 dr
30 mL
2 tbs = 1 oz
1 oz
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Equivalent Volume
Measurements (con’t)
Metric
Household
Apothecary
240 mL
8 oz = 1 c
8 oz
480 mL
2 c = 1 pt
16 oz
960 mL
2 pt = 1 qt
32 oz
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Table 3-8 Equivalent Weight
Measurements
Metric
Apothecary
60 mg
gr i (1 grain)
30 mg
1
gr ss ( 2 grain)
15 mg
gr 1
4
gr 1
60
1 mg
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Table 3-8 Equivalent Weight
Measurements (con’t)
Metric
Apothecary
1 g (1000mg)
gr xv (15 grains)
0.5 g
gr viiss (7 21 grains)
1 kg
2.2 lb
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Conversion Factors
 Conversion factor is a fraction made
of two quantities that are equal to
one another but which are expressed
in different units.
 Refer back to Table 3-8.
 1 kg and 2.2 lb are equal
 Two different conversion factors can
be formed.
 1 kg/2.2 lb and 2.2 lb/1 kg
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Using Conversion Factors
When writing a conversion factor:
1. The two quantities in the conversion
factor must be equal to one another.
2. The quantity containing the units that you
wish to convert to goes in the numerator
of the conversion factor.
3. The quantity containing the units that you
are converting from goes in the
denominator of the conversion factor.
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Using Conversion Factors (con’t)
Example
Write a conversion factor
for converting from
milliliters to ounces
Put ounces as the numerator
The correct conversion factor is
1 oz
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30 mL
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Using Conversion Factors:
Fraction Proportion Method
Procedure Checklist
3-1: Converting by the Fraction Proportion
Method
1. Write a conversion factor with the units that you are
converting to in the numerator and the units you are
converting from in the denominator.
2. Write a fraction with the unknown, “?”.
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Using Conversion Factors:
Fraction Proportion Method
Procedure Checklist (con’t)
3-1: Converting by the Fraction Proportion
Method
3. Set the two fractions up as a proportion.
4. Cancel units.
5. Cross-multiply, then solve for the unknown value.
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Review and Practice
How many kg does a 62-pound
child weigh?
62 lb = 2.2 lb
? kg 1 kg
62 x 1 = ? x 2.2
62 = 2.2 x ?
28.18 = ?
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Using Conversion Factors:
Ratio Proportion Method
Procedure Checklist
3-2: Converting by the Ratio Proportion
Method
1. Write a conversion factor as a ratio A:B so that A has
the units of the value that you are converting.
2. Write the second C:D so that C is the
missing value and D is the number that is
being converted.
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Using Conversion Factors:
Ratio Proportion Method
Procedure Checklist (con’t)
3-2: Converting by the Ratio Proportion
Method
3. Write the proportion in the form A:B::C:D.
4. Cancel units.
5. Solve the proportion by multiplying means and
extremes.
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Review and Practice
How many kg does a 66-pound
child weigh?
1 kg = 2.2 lb
First ratio is 1 kg:2.2 lb
Second ratio is ?:66
1 kg:2.2::?:66
Solve for missing value
?=30 kg
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Using Conversion Factors:
Dimensional Analysis
Procedure Checklist
3-3: Converting using the Dimensional
Analysis Method
1. Determine the unit of measure for the answer and place
it as the unknown on one side of the equation.
2. On the other side of the equation, write a
conversion factor with the units of
measure for the answer on top and the
units you are converting from on the
bottom.
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Using Conversion Factors:
Dimensional Analysis
Procedure Checklist (con’t)
3-3: Converting using the Dimensional
Analysis Method
3. Multiply the numerator of the conversion factor by the
number that is being converted.
4. Cancel units on the right side of the equation. The
remaining unit of measure on the right side of the
equation should match the unknown unit of measure on
the left side of the equation.
5. Solve the equation.
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Review and Practice
Convert 66 lb into kilograms.
1 kg = 2.2 lb
?/kg=1 kg/2.2 lb
?kg = 66 lb x 1 kg
2.2 lb
? = 30 kg
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Review and Practice
 You are instructing a patient to take 10
mL of medication at home, using a
calibrated teaspoon to measure the
medication. How many teaspoons should
the patient use?
10 mL:? tsp::5 mL:1 tsp
? x 5 = 10 x 1
5 x ? = 10
?=2
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Review and Practice
Convert the measures from one system
of measurement to another.
6 oz = ? mL
Answer = 180 mL
Your patient is to receive 1.5 tbs
of medicated mouthwash. How
many cc of medicated mouthwash
should the patient receive?
Answer = 22.5 mL
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Temperature
 Both Fahrenheit (F) and Celsius (C)
temperature scales are used in
health-care settings.
 Celsius temperature is also known as
Centigrade (C) temperature scale.
 Water freezes at
 32 degrees Fahrenheit
 0 degrees Centigrade
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Temperature
(con’t)
 Water boils at
 212 degrees Fahrenheit
 100 degrees Celsius
 Converting between these two
temperature scales is sometimes
necessary.
 Use formulas to convert between the
systems.
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Temperature
(con’t)
Converting Between Temperature
Systems
 To convert from F to C use:
°F- 32 = °C
1.8
 To convert from C to F use:
(1.8 X °C) + 32 = °F
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Temperature
(con’t)
Converting Between Temperature
Systems
You can also use the formula
5F-160 = 9C
to convert between Fahrenheit and
Celsius.
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3-62
Review and Practice
Convert the temperatures.
35 0C = ? 0F Answer = 95 0F
103.6 0F = ? 0C Answer = 39.8 0C
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3-63
Time
 Traditional 12-hour clock
 It can be a source of errors in
medication administration.
 Each time occurs twice daily.
10:00
10:00
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a.m.
p.m.
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3-64
Time (con’t)
 24-hour clock
 Military or international time
 Each time occurs only once per
day
10:00
10:00
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a.m.
p.m.
= 1000
= 2200
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3-65
Time
(con’t)
When using a 24-hour clock for
international time:
1. Write 00 as the first two digits to
represent the first hour after midnight.
2. Write 01, 02, 03, … 09 as the first two
digits to represent the hours 1:00 a.m.
through 9:00 a.m.
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Time
(con’t)
3. Add 12 to the first two digits to
represent the hours 12:00 p.m.
through 11:00 p.m. so that 12, 13, 14,
…23 represent these hours.
4. Write midnight as either 2400
(international) or 0000 (military time).
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Review and Practice
Convert 9:00
time.
 9:00
a.m.
a.m.
to international
= 0900
Convert 12:19
time.
a.m.
to international
 12:19 a.m. = 0019
Convert 4:28 p.m. to international time.
 4:28 p.m. = 1628
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Review and Practice
(con’t)
Convert 1139 to traditional time.
 1139 = 11:39
a.m.
Convert 1515 to traditional time.
 1515 = 3:15
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p.m.
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3-69
International Time
To state the time using international time:
1. Say “zero” if the first digit is a zero.
2. Say “zero zero” if the first two digits
are both zero.
3. If the minutes are represented by
00, then say “hundred” after you say
the hour.
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Review and Practice
State the time 0900.*
Say “zero nine hundred.”
State the time 1139.*
Say “eleven thirty-nine.”
State the time 0023.*
Say “ zero zero twenty-three.”
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Review and Practice
Convert 5.0 mcg to mg.
5.0 mcg ÷ 1000 = 0.005 mg
Convert 43 kg to g.
43 x 1000 = 43,000 g
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Review and Practice
How many kg does an 88-pound
child weigh?
88 lb = 2.2 lb
? kg 1 kg
88 x 1 = ? x 2.2
88 = 2.2 x ?
40 kg = ?
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3-73
Review and Practice
Convert 50ºC to ºF.
(1.8 x 50) + 32 = ºF
(90) + 32 = ºF
122 = ºF
Convert 100ºF to ºC.
100  32  C
1.8
68  C
1.8
37.78  C
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3-74
Systems of Weights and Measures
As a pharmacy technician it is imperative
that you master the concepts of the
systems of measurements and weights.
You need to be able to “measure up to
the mark,” so to speak, as you will use
units of measurement and weight in all
dosage calculations.
THE END
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