48th Annual Meeting

7/20/2014
48th Annual Meeting
Metric System of Measurement
A Review of Pharmacy
Calculations for Pharmacy
Technicians
Base Unit
1 (g, L) =
Nina Pavuluri, Ph.D.





Review conversion of measurements within the metric
systems of weight and volume
Explain the processes of ratio and proportion,
percentage and dilution and concentration
Help understand intravenous flow rates, and solving
dosage problems
Reading, interpreting, and solving calculation
problems encountered in the preparation and
distribution of prescriptions/medication orders
Name
Symbol
kilo
hecto
deka
base unit
deci
centi
milli
micro
k
h
da
(g, L)
d
c
m
mc, µ
nano
n
Common Conversions
I do not have a vested interest in or affiliation with
any corporate organization offering financial
support or grant monies for this continuing education
activity, or any affiliation with an organization
whose philosophy could potentially bias my
presentation
Objectives
0.001
0.01
0.1
1
10
100
1000
1000000 or 106
1000000000 or 109
Navigating the Oceans of Opportunity
Disclosure
Factor
Apothecary
Metric
1 grain
64.8mg
Commonly used
equivalents
65mg
1 ounce
31.1g
30g
1 pound (lb)
1 minim
373.2g
0.062mL
454g
0.06mL
1 fluid ounce
29.57mL
30mL
128 fluid ounce
3785mL
1 gallon
2.2lb
1kg
Conversions and Dimensional
Analysis


Identify the quantity to be converted as well as any
conversion factors that you will need.
Terms that are equal to each other may be written
in the form of a fraction.
mcg
0.1mg
?
mL
mL
1000mcg
0.1mg *
 100mcg
1mg
0.1mg 100mcg

mL
mL
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7/20/2014
Examples

Percentages
Convert 1g/dL to g/mL
1000mL 1L
1dL *
*
 100mL
1L
10dL
1g
1g

 1%w / v
dL 100mL

Percent weight -in-volume, %w/v is number of grams
in 100mL
0.9% w / v 
0.9 g
100mL
Eg.: A certain injectable contains 2mg of a drug per mL
solution. What is the strength expressed in %w/v?
Express weight in gram
2mg *
1g
 0.002g
1000mg
Set up the proportion and solve for the unknown
0.002g
?g
0.002g

or simply
*100mL
1mL
100mL
mL
=0.2g/100mL= 0.2%w/v= 0.2g/dL
Ratio and Proportion
Percentages
 Used when two expressions are directly related to
one another
Eg: How many mg of Demerol is present in 5mL when
there is 15mg of Demerol in 1mL?

15mg ? mg

1mL
5mL
? mg 

Eg.: How many grams of dextrose must be added to
475mL of water to make a 65% (w/w) solution?
65g
xg

(x  475)g 100g
100x  65x  30875
x  882.14g
15mg * 5mL
 75mg
1mL
Ratio and Proportion
A child weighing 28 lb is to receive 4 mg of phenytoin per
kilogram of body weight daily as an anticonvulsant (Dose=
4mg/kg/day). How many milliliters of pediatric phenytoin
suspension containing 30 mg per 5 ml should the child receive
per day?
4mg ? mg

; =50.909mg
2.2lb 28lb
30mg 50.909mg
Source;

5mL
? mL
 8.48mL  8.5mL
Percent weight -in-weight, %w/w
number of grams in 100g
Percentages

Percent volume -in-volume, %v/v
number of milliliters in 100mL
Eg.: A dermatologic lotion contains 1.25mL of liq.
Phenol in 500mL. Calculate the percentage strength
(%v/v) for the label.
1.25mL
? mL

500mL 100mL
 0.25%v / v
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Percentages


Dilution and Concentration
Milligram percent, mg%
number of milligrams in 100mL
Gram per deciliter = %w/v
number of grams in 100mL
Dilution and Concentration
Eg.: Rx Clindamycin Phosphate 1.5%
Alcohol (52% v/v) qs ad 120mL
The pharmacy has no clindamycin phosphate powder
but does have clindamycin phosphate sterile solution,
150mg/mL in vials. From the label, the technician
learns that the solution is aqueous.
a)How many mL of the clindamycin phosphate sterile
solution should the technician use in filling the
prescription?
b)How many mL of 52% alcohol is required?
Contd.
Source
S ou rce
a)
P r oduct
C 1Q 1  C 2 Q 2
Pr oduct
CsQs  C pQ p
150mg / mL *Qs  1.5% *120mL
The units should be the same on both sides of the equation
1500mg
1.5g

 15mg / mL
1.5% =
100mL 100mL
150mg / mL *Qs  15mg / mL *120mL
How many mL of a 100mg/mL concentrate of Rhus
toxicodendron extract should be used to prepare the
following prescription?
Rx
Rhus Toxicodendron extract 10μg/mL
Sterile water for injection qs 100mL
Sig: As directed

Qs  12mL
b)Volume contraction is observed, when alcohol and water
(aqueous solutions) are mixed. Hence, it is strongly advised
that the volume of alcohol required be not calculated by
subtracting the volume of source from the total volume
of the prescription. A sufficient volume of alcohol (qs)
is used to make up the final volume.
Contd.
Reconstitution of Powders
Source
Pr oduct

CsQs  C pQp
[100mg / mL]*Q p  10 g/ mL*100mL
Units should be the same on both sides of the equations
1mg
 0.01mg
10g*
1000  g
[100mg / mL]*Q p  0.01mg / mL*100mL



Certain medications including antibiotics are
unstable when stored in solution form
Dry powders must be reconstituted with a sterile
diluent
Instructions are supplied indicating the volume of
diluent to be added
Powdered drug may/may not contribute to the final
volume
Qp  0.01mL of concentrate
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7/20/2014
Example

Rate of flow
A pharmacy receives a medication order to
prepare 600,000 units of penicillin G sodium to be
added to 1L of D5W. A vial of penicillin G sodium
containing a million units is on hand and the
directions on the vial state” Add 4.6mL sterilized
water for 200,000 units/mL”. How many mL of the
reconstituted solution must be added to the 1L D5W
bag?
Rate of Flow (R) 
Proportion;
200,000 units 600,000units

; 3mL
? mL
1mL
Withdraw 3mL of the reconstituted solution using a syringe
Add to the 1L D5W
Rate of Flow of Intravenous Fluids
(drops per min)
IV fluids: For adequate hydration of patients or
sometimes for administering potent medications
(Medicated IV drips). Usually operated by IV
infusion pumps.
Example

Eg.:
An intravenous fluid of 1000 ml of Ringer’s Injection
was started in a patient at 8:00 A.M. and was
scheduled to run for 12 hrs. At 3:00 P.M. it was found
that 800 ml of the fluid remained in the bottle. At
what rate of flow should the remaining fluid be
regulated using an IV set that delivers 15 drops per ml
in order to complete the administration of the fluid in
the scheduled time?
Contd.


Fluid remaining: 800mL; Time remaining
5hr=300minutes
Formula Method
Rate 

Drop Factor: drops/ml



Standard IV solution sets: 10-15 gtt (drops) per ml
Microdrip sets; Drop factor :60 gtt/ml.
t
R = rate of flow (gtt/min)
V = total volume to be infused (ml)
D = drop factor (gtt/ml)
t = total time of infusion (in minutes)
Contd.
Take 4.6mL of sterilized water (as per instructions on the vial)
Add to the powder in the vial and shake well
Source: 200,000 units/mL
VD
V * D 800mL *15gtt / mL

 40gtt / min
t
300min
Proportion Method
800mL ? mL

; 2.67mL
300min 1min
? gtt
15gtt

; 40gtt
1mL 2.67mL
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Contd.

Example
Dimensional Analysis
?

gtt
gtt
1
 800mL *15
*
 40gtt / min
min
mL 300min
How many mEqs of Ca2+ are represented in a
solution containing 140mg CaCl2.2H2O in 100mL?
(Mol. Wt. 147)
# mEq 
=
Milliequivalents




Electrolytes in TPNs to correct electrolyte imbalance
Expressed in units known as milliequivalents (mEq)
Measure of the chemical activity of an electrolyte
Related to ionic charges and takes valence into
consideration
Equations
wt. in mg *valence
Mol.wt.
140 * 2
147
 1.9mEq
Total Parenteral Nutrition


Large volume parenteral fluids containing essential
nutrients
Include vitamins, trace minerals, antibiotics and
other medications
TPNs
Mol. wt.
valence
wt. in mg
# mEq =
mEq wt.
mEq wt. =
wt. in mg *valence(charge)
# mEq 
Mol.wt.
TPN Solution Formula
Component Source
Calcium gluconate 2.5mEq
10mL vial containing 12 mEq
Heparin 1000 units
5 mL vial containing
500units/mL
20mL vial containing 25%
solution
Sodium chloride 30mEq
To be added to:
500mL of 50% dextrose injection
500mL of 8.5% amino acids injection
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7/20/2014
Contd.
Milliequivalents Example
You have been instructed to add 15 mL of sodium
chloride to a patient’s IV bag. Using the label shown,
calculate how many milliequivalents of sodium chloride
will be in 15 mL of solution.
Calcium gluconate:
12mEq 2.5mEq

; 2.08mL
? mL
10mL
Heparin :
500unit 1000unit

; 2mL
1mL
? mL
Sodium chloride:
Solution 1: Using the ratio-proportion method,
25g
 5g
Source  20mL of 25% = 20mL of
100mL
wt.in mg*valence 5000 *1
# mEq 

 85.47mEq
Mol.wt.
58.5
85.47mEq 30mEq

; 7.02mL
? mL
20mL
4mEq ? mEq

; 60mEq
1mL
15mL
Proportion Example
Unit Calculation Example
How many milligrams of medication
are in 6 mL of the solution shown in this
label?
A patient is to receive a bolus (concentrated) dose of
heparin. If the dose is 7500 units and you have a vial
with the label shown, how many milliliters will you
prepare?
Solution 1: Using5000units
the ratio-proportion
method,
7500units
20mg ? mg

; 60mg
2mL 6mL
1mL
Percentage Strength Example

? mL
; 1.5mL
Infusion Rate
If there are 30 g of dextrose in 500 mL of the solution,
what is the percentage of solution?
If there is a flow rate of 40 gtt/min using a 15 drop
set, how many liters will be delivered over 24 hours?
Solve by using the30g
equation: ? g
Solution 2: This problem can also be calculated using
V *D
the dimensional analysis method.

500mL 100mL
6g /100mL  6%
;6g
R
t
V *15gtt / mL
40gtt / min 
24 * 60 min
1L
V  3840mL *
 3.84L
1000mL
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7/20/2014
Questions?
7

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