pharm. calculations exam 1 Flashcards
International System of Units
International System of Units (SI)
SI; French abbr. for Système International (d’unités)
Formerly, the metric system
Internationally recognized/accepted system of weights and measures
Widely used in the regulatory, healthcare and manufacturing sector in the US
International System of Units – cont’d
what are the units for length, weight and volume
The fundamental/primary/base units of the SI are:
Meter (m) for length
Kilogram (kg) for weight
Liter (L) for volume
Multiples and fractions/subdivisions of these base units may be derived using prefixes to denote their relative values (see tables on next slide)
International System of Units – cont’d
atto
femto
pic
nano
micro
milli
centi
deci
deca
hecto
klo
myria
mega
giga
tera
peta
exa
atto - one quintillionth (10^-18)
femto - one quadrillionth (10^-18)
pico - one trillionth
nano - one-billionth
micro - one millionth
milli - one thousandth
centi - one hundredth
deci - one tenth
deca - 10 x
hecto - 100 x
kilo - 1000 x
myria - 10,000 x
mega - 1 million x
giga - 1 billion x
tera - 1 trillion x
peta - 1 quadrillion x
exa - 1 quintillion
Guidelines for the Correct Use of the SI
Generally, the U.S. Metric Association recommends the following as relates to the use of SI units (as may apply to the practice of pharmacy):
Do not capitalize unit names and symbols, except when used at the beginning of a sentence or in headings. However, the symbol for a liter (L, l) may be capitalized or not.
For example, 4 g, and not 4 G; 4 mm, and not 4 MM; 4 L or 4 l
For decimals, use a decimal point (not a comma); for example, 4.5 mL, not 4,5 mL
No period after SI symbols, except at the end of a sentence. For example, 4 mL and 4 g, not 4 mL. and 4 g. respectively
Guidelines for the Correct Use of the SI – cont’d
Use a solidus (5 mL/h) or a negative exponent (5 mL.h−1), for a compound unit that is a ratio or quotient of two units
Do not combine symbols with spelled-out terms in the same expression, for example, 3 mg/mL, not 3 mg/milliliter
Unit symbols have no plural form, for example, 1 mg; 5 mg, 10 mL; “s” is added to spelled out names of units to obtain their plural form, for example, 1 milligram, 5 milligrams, 10 milliliters
Two unit symbols: mcg (often used in pharmacy practice) and μg (SI) are accepted for the microgram
Guidelines for the Correct Use of the SI – cont’d
what does cm^3 equal
The symbol for:
square meter is m^2
cubic centimeter is cm^3
The cubic centimeter (cm^3) is considered equivalent to a milliliter (mL)
Use decimal fractions (e.g. 5.25 g), not common fractions (5¼ g)
Always place a zero (0) in front of a leading decimal point (e.g. 0.5 g, not .5 g)*
Guidelines for the Correct Use of the SI – cont’d
Do not place “trailing” zeros after a whole number on prescriptions and medication orders (e.g. 5 mg, not 5.0 mg)
Select the unit that will result in a numeric value between 1 and 1000. For example:
500 g, not 0.5 kg
1.96 kg, not 1960 g
750 mL, not 0.75 L
Equivalents: Length, Volume, & Weight
1 inch = __ cm
1 meter = __ in
1 fluidounce (fl. oz) __ mL
1 pint (16 fl. oz) = ___ mL
1 quart (32 fl. oz) = ___ mL
1 gallon, US (128 fl. oz.) = ___ mL
1 pound (lb, avoirdupois) = ____ g
1 ounce (oz. avoirdupois) = ____ g
1 kilogram (kg) = 2.2 lb
1 lb = ___ oz
Table showing some important length, volume, and weight equivalents in pharmacy:
1 inch = 2.54 cm
1 meter = 39.37 in
1 fluidounce (fl. oz) = 29.57 mL
1 pint (16 fl. oz) = 473 mL
1 quart (32 fl. oz) = 946 mL
1 gallon, US (128 fl. oz.) = 3785 mL
1 pound (lb, avoirdupois) = 454 g
1 ounce (oz. avoirdupois) = 28.35 g
1 kilogram (kg) = 2.2 lb
1 lb = 16 oz
Measure of Length
1 kilometer (km) = _____ meters
1 hectometer = _____ meters
1 decameter = _____ meters
1 decimeter = _____ meters
1 centimeter = _____ meters
1 millimeter = _____ meters
1 micrometer = _____ meters
1 meter =
____ kilometer
___ hectometer
___ decameter
___ decimeter
___ centimeter
___ millimeter
___ micrometer
___ nanometer
The meter (m) is the base SI unit of length
The metric system is a “superset” of the SI, and conversions can be carried out according to the tables below:
1 kilometer (km) = 1,000,000 meters
1 hectometer = __100,000___ meters
1 decameter = _10,000____ meters
1 meter =
1 decimeter = _0.100____ meters
1 centimeter = _0.010____ meters
1 millimeter = _0.001____ meters
1 micrometer = _0.000,001____ meters
1 meter =
_0.001___ kilometer
_0.01__ hectometer
_0.1__ decameter
_10__ decimeter
_100__ centimeter
_1000__ millimeter
1,000,000___ micrometer
_1,000,000,000__ nanometer
Measure of Length – cont’d
Applications:
- Dimensions of a transdermal patch:
Example: A round transdermal patch measures 4.3 cm in diameter. Convert this dimension to inches and millimeters.
1.69 cm :)
43 mm
Measure of Length – cont’d
Applications:
Dose calculation on the basis of height (and/or weight, or body surface area):
Example: An injection containing 7.5 mg of leuprolide acetate is administered to a patient weighing 25 kg. Calculate the dose on a mcg/lb basis if 1 kg = 2.2 lb.
136.36 mcg/lb
Measure of Length – cont’d
Applications:
Determining the dimensions or area of a tumor to inform appropriate treatment
Example: A lung tumor measuring 2.1 cm was detected in a patient. What are the equivalent dimensions in millimeters and in inches?.
21 mm
0.8 in
Measure of Length – cont’d
Relationships and interconversions of linear measures:
Measure of Volume
The liter (L or l) is the base SI unit of volume
A liter is equivalent to the volume of:
cube of one-tenth of a meter: 0.1 m x 0.1 m x 0.1 m = 0.001 m3
a cubic decimeter: 1 dm x 1 dm x 1 dm = 1 dm3 (1 L)
10 cubic centimeters: 10 cm x 10 cm x 10 cm = 1000 cm3 (1000 mL)
Hence, 1 cubic centimeter (cc, cm3) is equivalent to 1 milliliter (mL)
- no need to memorize ths*
Measure of Volume – cont’d
Relationships and interconversions of metric volume:
1 kiloliter
Measure of Volume – cont’d
Applications:
Calculation and/or conversion of concentration of liquid medication
Example: The product of biotechnology, filgrastim (NEUPOGEN), is available in vials containing 0.3 mg of the drug in each milliliter.
Which choice is equivalent in concentration?
a. 0.03 mg/0.1 dL
b. 300 mcg/0.01 dL
c. 3 mcg/0.01 cL
d. 300 mcg/10 cL
B
Applications:
Dose calculation of liquids (medication, excipients, etc.)
Example: An injection contains 50 mcg/0.5 mL of drug. How many μL of the injection should be administered to deliver 0.04 mg of the drug
skip?
Applications:
Dose calculation of solids (medication, excipients, etc.)
Example: How many grams of digoxin (LANOXIN) would be required to make 25,000 tablets each containing 250 mcg of digoxin?
6,250,000mcg
6.25g
Weights & Measures
Weight:
- A measure of the gravitational force acting on a body, and is proportional to its mass
- Weight is affected by position (latitude and altitude), temperature, and pressure
- Mass is a constant and never changes
Measure:
- An estimation of the volume, coverage, level, or extent of matter
- Measures or volumes are affected by temperature and pressure
Weight: Systems of weight
Weight Measurements
Weighing is facilitated by the use of specialized equipment and accessories including:
- Balances or scales
- Weights
- Spatula
- Weighing paper, pans, dishes, or boats
The suitability of one or the other equipment to use for weighing depends on the:
- Sensitivity
- Accuracy
- Capacity of the equipment; as well as
- Type of material to be weighed
Prescription Balance
Definition: scales adapted to or designed for weighing the ingredients entering into medicinal formulas prescribed by physicians
The construction of the prescription balance must meet certain standards concerning:
Sensitivity
Accuracy
Balances can be classified based on design or construction to include:
Single-Beam Equal-Arm Balances
Unequal-Arm Balances
Compound-Lever Balances
Torsion Balances
just have to know not really on the exam
don’t memorize these!
Prescription Balance – cont’d
Single-Beam Equal-Arm Balance:
- Principle: metallic lever/beam
- Divided equally by central knife-edge
- Two end or peripheral knife-edges support pans at each end equidistant from the central knife-edge
Unequal-Arm Balances:
- Useful for weighing large amounts
- Operation based on the principle that at equilibrium, the force x distance to pivot/fulcrum at one end equals force x distance at the opposite end
Prescription Balance – cont’d
Compound-Lever Balances:
- Invented by French mathematician, Gilles Personne de Roberval
- Underlying mechanism is the use of parallel beams to ensure the equilibrium of weights notwithstanding the position of weights on pans (i.e. if A+B+C=D, the beams are balanced)
Torsion Balances:
- Torsion: the act of twisting or the state of being twisted, as related to one end of an object relative to another
- Principle: the torsion balance operates on the principle of tension or resistance
Prescription Balance – cont’d
Balances can also be classified on the basis of sensitivity to include:
Class A: this references all balances with a sensitivity requirement (SR) of 6 milligrams (0.1 grains) or less with no load, and with a load of 10 grams in each pan
Class B: this refers to all balances with a sensitivity requirement of more than 6 milligrams and less than 30 milligrams (0.5 grains)
Measures: Systems of Measures
1 fluid ounce
1 point
1 quart
1 gallon US
torsion balance parts
graduate beam
rider
dial knob
arrest knob (keeps arms stable so that you can add and move substances)
pans
leveling screw
weight: systems of weight
1 lb = ___ g
1 oz = ___ g
1 kg = ____ lb
1 lb = _454__ g
1 oz = _28.35__ g
1 kg = _2.2___ lb
1 fl oz = ___ mL
1 pint = ___ mL
1 quart = ___ mL
1 gallon = ___ mL
1 fl oz = _29.57__ mL
1 pint = _473__ mL
1 quart = _946__ mL
1 gallon = _3785__ mL
Least Weighable Quantity (LWQ)
This is the smallest quantity of a substance that can be determined within the limits of acceptable of the instrument of measure while maintaining the desired high precision
the equation for it:
LWQ = (Sensitivity Requirement (mg) x 100%)/acceptable error (%)
Aliquot Method: Solids (Weight)
Definition: A method of obtaining small weights of medicinal substances within the limits of accuracy by weighing larger amounts of substance, diluting it with an inert diluent, and then weighing a portion (aliquot) of the mixture that would contain the desired amount of the substance.
aliquot method example
Practice Problem:
Rx: Drug A 5 mg
Lactose qs 400 mg
Mix & Make Capsule #1
Question: For a Class A prescription balance (i.e. SR = 6 mg, acceptable percentage error = 5%) how would you weigh a 5-mg quantity of drug A using the aliquot method?
Step 1: Calculate the Least weighable quantity (LWQ) for the Class A balance
LWQ = Sensitivity Requirement (mg) x 100%
Acceptable Error (%)
LWQ (Drug A) = (6 mg x 100%)/5%
= 120 mg is the least amount that you
can weight, if it is less then it will be inaccurate
Step 2: Determine the weight of the final aliquot to be prepared (e.g. 120 mg)
NOTE: Thus, the aliquot contains 5 mg Drug A (Drug) and 115 mg lactose (Diluent)
NOTE: It is convenient to choose an amount that is a multiple of the amount of drug (5 mg) to be weighed (e.g. 120 mg, 125 mg, 150 mg, etc.)
Step 3: Determine the multiple factor (which is a multiple of 5, and when multiplied by 5 ≥ LWQ
= 120 mg/5 mg = 24, not a multiple of 5 so change 120 to 125
= 125 mg/5 mg = 25
Step 4: Estimate the total amount of Drug A (Drug) needed:
= 5 mg x 25 = 125 mg
Step 5: Calculate the total amount of Lactose (Diluent) needed as follows:
= 115 mg x 25 = 2875 mg
Step 6: Calculate the total amount of mixture (Drug + Diluent) needed as follows:
= 125 mg + 2875 mg = 3000 mg
Step 7: Determine the amount of aliquot that would provide the amount of Drug A needed to fill the prescription by dividing the total amount by the multiple factors:
= 3000 mg/25 = 120 mg
Answer: To prepare the prescription, weigh 120 mg of the mixture (aliquot) which would contain 5 mg of Drug A and 115 mg of lactose, and then add 280 mg of lactose (to make a total of 400 mg)
*what is the point of going through all that just to end up at 120 again? When you can just add the drug A amount and the lactose amounts together, subtract that by the amount of the total lactose to add to find out how much lactose to add in the end
