### Pickar Math Rules

```Summary of Text rules
Systems Of Measurements
Weight
Unit
Abbreviation
Equivalents
gram
g
1 g = 1,000 mg
milligram
mg
1 mg = 1,000 mcg = 0.001 g
microgram
mcg (or µg)
1 mcg = 0.001 mg = 0.000001 g
kilogram
kg
1 kg = 1,000 g
Volume
Unit
liter
milliliter
cubic
centimeter
Abbreviatio
n
L (or ℓ)
mL (or mℓ)
Equivalents
1 L = 1,000 mL
1 mL = 0.001 L = 1 cc
cc
1 cc = 1 mL = 0.001 L
Unit
Abbreviation
Equivalents
drop
teaspoon
gtt
t (or tsp)
5 mL
tablespoon
ounce (fluid)
ounce (weight)
cup
T (or tbs)
oz
oz
cup
pint
quart
pt
qt
1T=3t
2 T = 1 oz
1 lb = 16 oz
1 cup = 8 oz or
240mL
1 pt = 2 cups
1 qt = 4 cups = 2 pt
 Due
to information from our
clinical partners and the Board of
Nursing the following rule was
developed.
 We
will accept documentation in
the form of Roman numerals,
Arabic numbers, decimals as well
as fractions.
Chapter 4
MULTIPLY to convert from a larger unit
to a smaller unit, or move the decimal
point to the right.
 Example:
3 L = ? mL
 THINK: Larger to Smaller: (×)
 Equivalent: 1 L = 1,000 mL
 3 L = 3 ×1,000 or 3.000 = 3,000 mL
to convert from a smaller
unit to a larger unit, or move the
decimal point to the left.
 DIVIDE
 Example:
400 mg = ? G
 THINK: Smaller to Larger: ()
 Equivalent: 1 g = 1,000 mg
 400 mg = 400  1,000 or 400. =
0.4 g
 Rule
De sire damount
 Equivale ntthatmatchestheunknown  Q uantity
Matchingconversion
D
E  Q
M
Example
The physician ordered 125 mcg of
digoxin to be given daily. Digoxin was
supplied in 0.25 mg scored tablets. How
0.25mg x 1000mcg/mg = 250 mcg

125mcg
 1 tablet  0.5 tablets
250 mcg
1
in = 2.5 cm
 1 cup = 240 mL
 1 oz = 30 mL
 1kg = 2.2 lb
We will not be using the grain (gr)
measurement in our math
calculations.
 40
kg = ? Lb
40 kg X 2.2lb/kg = 88 lb
 66lb = ? kg
66lb  2.2 kg/lb = 30 kg
Remember you will round to tenths
when needed. Example 5.23 will be
rounded to 5.3
 40
cm = ? In
40 cm  2.5 cm/in =16 in
 32 in = ? cm
32 in x 2.5 cm/in = 80 cm
Conversions
AM
Int’l. Time
PM
Int’l Time
12:00 midnight
2400
12:00 noon
1200
1:00
0100
1:00
1300
2:00
0200
2:00
1400
3:00
0300
3:00
1500
4:00
0400
4:00
1600
5:00
0500
5:00
1700
6:00
0600
6:00
1800
7:00
0700
7:00
1900
8:00
0800
8:00
2000
9:00
0900
9:00
2100
10:00
1000
10:00
2200
11:00
1100
11:00
2300
time and international
time are the same hours starting
with 1:00 AM (0100) through 12:59
PM (1259).
 Minutes after 12:00 AM (midnight)
and before 1:00 AM are 0001
through 0059 in international time.
 Hours
starting with 1:00 PM through
12:00 AM (midnight) are 12 h
greater in international time (1300
through 2400)
 International time is designated by a
unique four-digit number (colon’s
are not used)
 Math
Tip between the hours of 1:00
PM (1300) and 12:00 AM (2400),
the equivalent international time;
subtract 1200 from international
time to convert to equivalent
 Example
1
3:00 PM = 3:00 + 1200 = 1500
 Example 2
2212 = 2212 – 1200 = 10:12 PM
 Convert
between Fahrenheit and
Celsius temperatures:
F  32
C 
1.8
F  1.8C  32
 Convert
95˚ F to Celsius (First
subtract 32 then divide the result by
1.8)
95-32
C=
1.8
63
C=
1.8
C = 35°
 Convert
35˚ C to Fahrenheit
F = 1.8  35+12
F = 63+12
F = 95°
Equipment Used in Dosage Measurement



Medicine cup 1 fluid ounce or 30mL
capacity for oral liquids.
Calibrated to measure teaspoons and
tablespoons
Amounts less than 2.5 mL need to be
measured in a smaller device, i.e. oral
syringe
30 mL = 1 ounce
5 mL = 1 teaspoon
15 mL = 1 tablespoon
 Used
quantities
 Useful in medication of children
quantities to liquid
 Dispense eye and ear medications
Calibrations read from top to the black
ring of the suction plunger
 Calibrated in milliliters for each tenth
 Maximum volume administered in any one
site is 3mL
 Larger volumes of medications can be
delivered in divided doses or added to IV
therefore, syringes with 5,6,10, and 12
mL may be used

Luerlock syringe hub
Plunger
Needle
Barrel
Rubber plunger tip
 Used
prior to injection
 Also
known as Tuberculin or TB
syringe
 Used to administer small doses
 Calibrated in hundredths of a
milliliter
 Used to give dosages of less than
0.5 mL
 Measurement
of units-100 insulin only
 Do not use with any other
medications
 Syringe may be a standard units100 or a Lo-dose units-100 for
smaller doses


The needle is protected by a shield
Safety syringes are used to protect from
injury




Needle’s gauge is it’s interior diameter. Lower
the number the larger the diameter; 18-gauge
needle is wider than a 22 gauge.
The gauge depends on the viscosity
(thickness) of the medication as well as the
site.
The viscous the solution and deeper injections
require larger needles (lower gauge number)
Injection site (area of tissue to be reached) will
determine the length to be used.
TYPE
AGE
NEEDLE
SIZE
GAUGE(G)
NEEDLE
LENGTH
MAXIMUM
INJECTION
AMOUNT
LOCATION
ID
All ages
al
25 to 26 G 1/4 to 5/8
0.1 mL
Interior aspect
of forearm
Subcut
1 to 12
months
23 to 27 G 5/8
0.5 mL
Fatty tissue
over lateral
thigh muscle
Subcut
12 months
23 to 27 G ½ to ¾
0.5 to
1mL
Fatty tissue
over anterior
lateral thigh
muscle,
triceps, or
abdomen
IM
Infant to
child
22 to 25 G 5/8 to 1
inch
0.5 to 1
mL
Vastus
Lateralis
IM
21 to 25 G 1 to 1 ½
inches
2 to 3 mL
0.5 to 1
mL
Ventroglueal
Deltoid
5/8 most
common
Understanding Drug Labels
 Brand,
Manufacturer’s name for a drug. It is
usually the most prominent word on
the drug label
 Generic
Established, nonproprietary name
appears directly under the brand
name. Sometimes it can be place
inside
 Brand
Name- Carafate
 Generic Name- Sucralfate
 Dosage
weight or amount of
drug provided in a specific unit
of measurement

20 mg/ 2mL
 Structure
and composition of drug
◦ Solid forms for oral use
◦ Injectable
◦ Suppositories
◦ Creams
◦ Patches
 Full
quantity contained in bottle or
vial
 Total number of tablets or other
solids
 Total fluid volume for liquids

30 mL multiple dose vial
 Warnings
◦ Examples
 Refrigerate at all times
 Keep in a dry place
◦ Manufacturer
◦ Pharmacies
 Check
expired
 Important
if drug is recalled
 Quickly identifies a particular
group of medication packages
 Classifies
drugs according to
potential for use and abuse
◦ Schedule I – highest potential for
abuse
◦ Schedule V – lowest potential for
abuse
 Manufacturer
 National
 Bar
Code
 Review
Drug Code
p 138 & 139
practice on page 142148 Review set 21questions
Oral Dosage Calculations
Step 1 Convert
Be sure that all measurements are in the
same system and all units are in the
same size, converting when necessary
 Step 2 Think
Carefully consider what is the reasonable
 Step 3 Calculate Dosage




Ordered: Flagyl 0.75 g p.o t.i.d
You need to convert the 0.75 g to mg prior to
calculating amount that you will be
0.75 g = 750 mg
D desired
 Q (quanity) X
H (have)
D
750 mg
Q
x 1 t ablet
500 mg
H
Math Tips
 When solving dosage problems for drugs
supplied in tablets or capsules, Q
(quantity) is always 1 because the supply
dosage is per 1 tablet or capsule.
Therefore, Q = 1 tablet or capsule
 The maximum number of tablets or
capsules for a single dose is usually 3.
 Do
not always rely on a formula.
 Always estimate what is a
reasonable amount of the drug to
 This helps to identify if the
dosages calculated are reasonable
and sound.
Chapter 11
 Routes
 Intramuscular (IM)
 Subcutaneous (SC)
◦ Intravenous (IV)
Maximum dosage
 Average 150 lb adult = 3 mL
 Maximum for deltoid site is 2
 Children age 6-12 years = 2 mL
 Children birth to age 5 years = 1
mL
Parenteral dosages
 Round amount to be administered
to tenths if amount greater than 1
mL . Use a 3 mL syringe
 Amounts less than 1 mL rounded
to hundredths. Use a 1 mL syringe
for all amounts less than 0.5 mL
Parenteral dosages
 Amounts of 0.5 mL to 1 mL
calculated in tenths can be
accurately measured in either a 1
mL or a 3 mL syringe
Concentration
Type
Expiration Date
Brand Name
Manufacturer
Species
Generic Name
Storage
 Supply
dosage of insulin is 100
units per mL
 Abbreviated on label as U-100
 Syringe must also be U-100
 Accuracy
is critical
 Nurses must understand and
correctly interpret insulin order
and label
 The correct syringe must be
selected
40 units
NPH
Units-100
insulin
12 units
Regular
Units -100 insulin
Total insulin dosage = 52 units
1. Inject
30 units
of air.
2. Inject
10 units
of air.
3. Withdraw
10 units
regular.
4. Withdraw
30 units
NPH for a
total of 40
units.
1)
Inject 30
U air
2)
Inject 10 U
air
3)
Withdraw
10 U
Regular
4)
Withdraw
30 U NPH
For a total of
40 U
Chapter 12
When a fraction expresses the strength of a
solution, made from a liquid concentration
1. The numerator of the fraction is the number
of parts of the solute.
2. The denominator of the fraction is the total
number of parts of the solution.
3. The difference between the denominator(final
solution) and the numerator (parts of solute)
is the number of parts of solvent.

 Solute-
a concentrated or solid
substance to be dissolved or
diluted.
 Solvent- is the diluent used to
dissolve the solute
 Solution- the resulting mixture of a
solute plus a solvent
Example ¼ strength reconstituted OJ made from
canned frozen concentrate
¼ strength =1 part frozen juice concentrate
4 parts total reconstituted OJ
 1 part -OJ concentrate (solute, numerator)
 4 parts- total reconstituted OJ ( solution,
denominator)
 4-1 = 3 parts water (solvent)
Example 1 ⁄ 3 strength formula
1
part concentrate formula (solute)
 3 parts total solution
 3-1= 2 parts solvent (water)
Remember to convert all fluids to the
same equivalent when necessary.
 Example: Order Ensure ¼ strength
120mL for 3 feedings (Stock 4 fl oz can)
 Step 1 convert fluid to same equivalent
4 fl oz x 30mL/fl oz = 120mL ensure
concentrate

Step 2 calculate solute, solvent, and total
solution
 1 part solute(ensure) of 360 = 90 mL
 4 parts solution ( solute and solvent)
(3 feeding of 120 mL ¼ feeding = 120 x
3= 360 mL)
 4-1= 3 parts solvent 270mL
Chapter 14


Convert child’s weight from lb.'s to kg’s and
Example
45lb ÷ 2.2 lb/kg= 20.45 rounded to 20.5
Example
Convert 10 lb 12 oz to kg
First convert ounces to lb
12 oz ÷16 oz/lb= 12/16 = ¾ lb= 0.75 lb
10.75 lb ÷ 2.2 lb/kg = 4.88 rounded to 4.9
Second step: multiply mg/kg by child’s weight
in kg.
 Example
Order Morphine Sulfate 0.05 mg/kg per dose
Childs weight 35.9 kg
0.05 mg/kg/dose x 35.9 kg = 1.79 mg/dose
Rounded to 1.8 mg/dose

Chapter 15

Peripheral
◦ Rate of infusion should not exceed 200 mL in one
hour

Central line
◦ Accommodates larger concentrations and volumes
of fluid

Regulate an IV volume by electronic infusion
pump or controller calibrated in mL per hour
TotalmL ordered
 mL/h
Totalh ordered
(rounded to a whole number)

Order reads: D5W 250 mL IV over the next
two hours by infusion pump
Step 1: Think
•Pump is set by the rate of mL per
hour
•So, if 250 mL is to be infused in
two hours, how much will be
infused in one hour?
• Step 2: Use the formula:
T otalm L ordered
 m L/h
T otalh ordered
250 m L 125 m L

2h
1h
– Set pump at 125 mL per hour
– Set total volume to infuse at 250 mL
TotalmL ordered
 60 min/h mL/h
Totalminordered
(rounded to a whole number)
 Order:
◦ Ampicillin 500 mg IV in 50 mL
D5NS to infuse over 30 min via
infusion pump
 50mL
X 60 min/h = 100 mL/h
30 min
 Set
infusion pump to infuse at
100 mL/h with an infusion volume
of 50 mL
 Step
1: Calculate infusion volume for
1h (Volume ordered ÷by number of
hours to infuse) round this answer to
a whole number
 Step 2: V x Drop factor= qtt/min
T
 Physician
orders:
◦ D5W IV at 125 mL per hour
 Infusion set is calibrated for a drop
factor of 10 drops per mL
 Calculate IV flow rate in drops per
min
 Notice that the mL cancel out,
leaving drops per min
1
125mL
125 mL 10 gtt
 10 gtt/mL

60 min
60 min 1mL
6
 20.8 gtt/min
roller clamp to deliver 21 drops per min
 Order:
 Drop
D5W NS IV at 50 mL per h
factor is 60 drops per mL
 Notice order, 50 mL per hour, is the
same as the flow rate of 50 drops
per min when drop factor is 60
drops per mL
50 mL
 60 gtt per mL
60 min
 50 drops per min
```