Transcript Slide 1

Chapter 5
Basic Pharmaceutical
Measurements and
Calculations
Learning Objectives
• Describe four systems of measurement
commonly used in pharmacy, and be able to
convert units from one system to another.
• Explain the meanings of the prefixes most
commonly used in metric measurement.
• Convert from one metric unit to another (e.g.,
grams to milligrams).
• Convert Roman numerals to Arabic numerals.
Learning Objectives
• Distinguish between proper, improper, and
compound fractions.
• Perform basic operations with fractions,
including finding the least common denominator;
converting fractions to decimals; and adding,
subtracting, multiplying, and dividing fractions.
Learning Objectives
• Perform basic operations with proportions,
including identifying equivalent ratios and
finding an unknown quantity in a proportion.
• Convert percents to and from fractions and
ratios, and convert percents to decimals.
• Perform elementary dose calculations and
conversions.
• Solve problems involving powder solutions and
dilutions.
• Use the alligation method.
SYSTEMS OF PHARMACEUTICAL
MEASUREMENT
• Metric System
• Common Measures
• Numeral Systems
BASIC MATHEMATICS USED IN
PHARMACY PRACTICE
• Fractions
• Decimals
• Ratios and Proportions
COMMON CALCULATIONS IN
THE PHARMACY
• Converting Quantities between the Metric and
Common Measure Systems
• Calculations of Doses
• Preparation of Solutions
SYSTEMS OF PHARMACEUTICAL
MEASUREMENT
• Metric System
• Common Measures
• Numeral Systems
Measurements
in the Metric System
(a) Distance or length
(b) Area
(c) Volume
Table 5.1
Système International Prefixes
Prefix
Meaning
micro-
one millionth (basic unit × 10–6, or unit × 0.000,001)
milli-
one thousandth (basic unit × 10–3, or unit × 0.001)
centi-
one hundredth (basic unit × 10–2, or unit × 0.01)
deci-
one tenth (basic unit × 10–1, or unit × 0.1)
hecto-
one hundred times (basic unit × 102, or unit × 100)
kilo-
one thousand times (basic unit × 103, or unit × 1000)
Table 5.2
Common Metric Units: Weight
Basic Unit
Equivalent
1 gram (g)
1000 milligrams (mg)
1 milligram (mg)
1 kilogram (kg)
1000 micrograms (mcg),
one thousandth of a gram (g)
1000 grams (g)
Table 5.2
Common Metric Units: Length
Basic Unit
Equivalent
1 meter (m)
100 centimeters (cm)
1 centimeter (cm)
0.01 m
10 millimeters (mm)
0.001 m
1 millimeter (mm)
1000 micrometers
or microns (mcm)
Table 5.2
Common Metric Units: Volume
Basic Unit
Equivalent
1 liter (L)
1000 milliliters (mL)
1 milliliter (mL)
0.001 L
1000 microliters (mcL)
Measurement and Calculation Issues
Safety Note!
It is extremely important that
decimals be written properly. An
error of a single decimal place is an
error by a factor of 10.
Table 5.3
Common Metric Conversions
Conversion
Instruction
Example
kilograms (kg) to
grams (g)
multiply by 1000 (move decimal
point three places to the right)
6.25 kg = 6250 g
grams (g) to
milligrams (mg)
multiply by 1000 (move decimal
point three places to the right)
3.56 g = 3560 mg
milligrams (mg) to
grams (g)
multiply by 0.001 (move decimal
point three places to the left)
120 mg = 0.120 g
Table 5.3
Common Metric Conversions
Conversion
Instruction
Example
liters (L) to
milliliters (mL)
multiply by 1000 (move
decimal point three places to the 2.5 L = 2500 mL
right)
milliliters (mL) to
liters (L)
multiply by 0.001 (move
decimal point three places to the 238 mL = 0.238 L
left)
Table 5.4
Apothecary Symbols
Volume
Unit of measure
Weight
Symbol
Unit of measure
minim
♏
grain
fluidram
fℨ
scruple
fluidounce
f℥
dram
pint
pt
ounce
quart
qt
pound
gallon
gal
Symbol
gr
Э
ℨ
℥
℔ or #
Table 5.5
Apothecary System: Volume
Measurement Unit
Equivalent within System
Metric Equivalent
1♏
0.06 mL
16.23 ♏
1 mL
1 fℨ
60 ♏
5 mL (3.75 mL)*
1f ℥
6 fℨ
30 mL (29.57 mL)†
1 pt
16 f ℥
480 mL
1 qt
2 pt or 32 f ℥
960 mL
1 gal
4 qt of 8 pt
3840 mL
* In reality, 1 fℨ contains 3.75 mL; however that number is usually rounded up to 5 mL or
one teaspoonful
†In reality, 1 f℥, contains 29.57 mL; however, that number is usually rounded up to 30
mL.
Table 5.5
Apothecary System: Weight
Measurement Unit
1 gr
15.432 gr
1Э
1ℨ
1℥
1#
Equivalent within System
20 gr
3 Э or 60 gr
8 ℨ or 480 gr
12 ℥or 5760 gr
Metric Equivalent
65 mg
1g
1.3 g
3.9 g
30 g (31.1 g)
373.2 g
Measurement and Calculation Issues
Safety Note!
For safety reasons, the use of the
apothecary system is discouraged.
Use the metric system instead.
Table 5.6
Avoirdupois System
Measurement Unit
1 gr (grain)
1 oz (ounce)
1 lb (pound)
Equivalent within System
Metric Equivalent
437.5 gr
16 oz or 7000 gr
65 mg
30 g (28.35 g)*
1.3 g
* In reality, an avoirdupois ounce actually contains 28.34952
g; however, we often round up to 30 g. It is common
practice to use 454 g as the equivalent for a pound (28.35 g
× 16 oz/lb = 453.6 g/lb, rounded to 454 g/lb).
Table 5.7
Household Measure: Volume
Measurement Unit
Equivalent within System
1 tsp (teaspoonful)
Metric Equivalent
5 mL
1 tbsp (tablespoonful)
3 tsp
15 mL
1 fl oz (fluid ounce)
2 tbsp
30 mL (29.57 mL)*
1 cup
8 fl oz
240 mL
1 pt (pint)
2 cups
480 mL*
1 qt (quart)
2 pt
960 mL
1 gal (gallon)
4 qt
3840 mL
*
In reality, 1 fl oz (household measure) contains less than 30 mL; however, 30 mL
is usually used. When packaging a pint, companies will typically present 473 mL,
rather than the full 480 mL, thus saving money over time.
Table 5.7
Household Measure: Weight
Measurement Unit
1 oz (ounce)
1 lb (pound)
2.2 lb
Equivalent within System
16 oz
Metric Equivalent
30 g
454 g
1 kg
Measurement and Calculation Issues
Safety Note!
New safety guidelines are
discouraging use of Roman
numerals.
Table 5.8
Comparison of Roman and
Arabic Numerals
Roman
Arabic
Roman
Arabic
ss
0.5 or 1/2
L or l
50
I or i or i
1
C or c
100
V or v
5
D or d
500
X or x
10
M or m
1000
Terms to Remember
• metric system
• meter
• gram
• liter
BASIC MATHEMATICS USED IN
PHARMACY PRACTICE
• Fractions
• Decimals
• Ratios and Proportions
Fractions
• When something is divided into parts, each
part is considered a fraction of the whole.
Fractions
• When something is divided into parts, each
part is considered a fraction of the whole.
• If a pie is cut into 8 slices, one slice can be
expressed as 1/8, or one piece (1) of the
whole (8).
Fractions of the Whole Pie
Fractions
If we have a 1000 mg tablet,
• ½ tablet = 500 mg
• ¼ tablet = 250 mg
Terminology
fraction
a portion of a whole that is
represented as a ratio
Fractions
Fractions have two parts,
Fractions
Fractions have two parts,
• Numerator (the top part)
1
8
Fractions
Fractions have two parts,
• Numerator (the top part)
• Denominator (the bottom part)
1
8
Terminology
numerator
the number on the upper part of
a fraction
Terminology
denominator
the number on the bottom part of
a fraction
Fractions
A fraction with the same numerator and same
denominator has a value equivalent to 1.
In other words, if you have 8 pieces of a pie
that has been cut into 8 pieces, you have 1 pie.
8
1
8
Discussion
What are the distinguishing
characteristics of the following?
• proper fraction
• improper fraction
• mixed number
Remember
The symbol > means “is greater than.”
The symbol > means “is less than.”
Terminology
proper fraction
1
1
4
• a fraction with a value of less
than 1
• a fraction with a numerator
value smaller than the
denominator’s value
Terminology
improper fraction
• a fraction with a value of
larger than 1
• a fraction with a numerator
value larger than the
denominator’s value
6
1
5
Terminology
mixed number
a whole number and a fraction
1
5
2
Adding or Subtracting
Fractions
When adding or subtracting fractions with
unlike denominators, it is necessary to
create a common denominator.
Adding or Subtracting
Fractions
When adding or subtracting fractions with
unlike denominators, it is necessary to
create a common denominator.
This is like making both fractions into the
same kind of “pie.”
Terminology
common denominator
a number into which each of the
unlike denominators of two or
more fractions can be divided
evenly
Remember
Multiplying a number by 1 does not change
the value of the number.
5 1  5
Therefore, if you multiply a fraction by a
fraction that equals 1 (such as 5/5), you do
not change the value of a fraction.
5 5  5
5
Guidelines for Finding a
Common Denominator
1. Examine each denominator in the given
fractions for its divisors, or factors.
Guidelines for Finding a
Common Denominator
1. Examine each denominator in the given
fractions for its divisors, or factors.
2. See what factors any of the denominators
have in common.
Guidelines for Finding a
Common Denominator
1. Examine each denominator in the given
fractions for its divisors, or factors.
2. See what factors any of the denominators have
in common.
3. Form a common denominator by
multiplying all the factors that occur in all
of the denominators. If a factor occurs more
than once, use it the largest number of times
it occurs in any denominator.
Example 1
Find the least common denominator of
the following fractions
Step 1. Find the prime factors (numbers divisible only by 1 and
themselves) of each denominator. Make a list of all the different
prime factors that you find. Include in the list each different factor
as many times as the factor occurs for any one of the denominators
of the given fractions.
The prime factors of 28 are 2, 2, and 7 (because 2 3 2 3 7 5
28). The prime factors of 6 are 2 and 3 (because 2 3 3 5 6).
The number 2 occurs twice in one of the denominators, so it
must occur twice in the list. The list will also include the unique
factors 3 and 7; so the final list is 2, 2, 3, and 7.
Example 1
Find the least common denominator of
the following fractions
Step 2. Multiply all the prime factors on
your list. The result of this multiplication is
the least common denominator.
Example 1
Find the least common denominator of the
following fractions
Step 3. To convert a fraction to an equivalent fraction
with the common denominator, first divide the least
common denominator by the denominator of the
fraction, then multiply both the numerator and
denominator by the result (the quotient).
The least common denominator of 9⁄28 and 1⁄6 is
84. In the first fraction, 84 divided by 28 is 3, so
multiply both the numerator and the denominator by 3.
Example 1
Find the least common denominator of
the following fractions
In the second fraction, 84 divided by 6 is 14, so
multiply both the numerator and the
denominator by 14.
Example 1
Find the least common denominator of
the following fractions
The following are two equivalent fractions:
Example 1
Find the least common denominator of
the following fractions
Step 4. Once the fractions are converted to
contain equal denominators, adding or
subtracting them is straightforward. Simply
add or subtract the numerators.
Multiplying Fractions
When multiply fractions, multiply the numerators
by numerators and denominators by
denominators.
Multiplying Fractions
When multiply fractions, multiply the numerators
by numerators and denominators by
denominators.
In other words, multiply all numbers above the
line; then multiply all numbers below the line.
Multiplying Fractions
When multiply fractions, multiply the numerators
by numerators and denominators by
denominators.
In other words, multiply all numbers above the
line; then multiply all numbers below the line.
Cancel if possible and reduce to lowest terms.
Discussion
What happens to the value of a
fraction when you multiply the
numerator by a number?
Discussion
What happens to the value of a
fraction when you multiply the
numerator by a number?
Answer: The value of the fraction
increases.
Discussion
What happens to the value of a
fraction when you multiply the
denominator by a number?
Discussion
What happens to the value of a
fraction when you multiply the
denominator by a number?
Answer: The value of the fraction
decreases.
Discussion
What happens to the value of a
fraction when you multiply the
numerator and denominator by the
same number?
Discussion
What happens to the value of a
fraction when you multiply the
numerator and denominator by the
same number?
Answer: The value of the fraction
does not change because you have
multiplied the original fraction by 1.
Multiplying Fractions
Dividing the denominator by a number is
the same as multiplying the numerator by
that number.
3  5 15 3


20
20 4
Multiplying Fractions
Dividing the numerator by a number is the
same as multiplying the denominator by
that number.
6
6 1


4  3 12 2
Dividing Fractions
To divide by a fraction, multiply by its
reciprocal, and then reduce it if necessary.
1
1 3 3

 3
1/ 3
1
1
Terms to Remember
• fraction
• numerator
• denominator
• proper fraction
• improper fraction
• mixed number
The Arabic System
The Arabic system is also called the decimal
system.
Terminology
Arabic numbers
The numbering system that uses
numeric symbols to indicate a
quantity, fractions, and decimals.
Uses the numerals 0, 1, 2, 3, 4,
5, 6, 7, 8, 9.
The Arabic System
The decimal serves as the anchor.
• Each place to the left of the decimal point
signals a tenfold increase.
• Each place to the right signals a tenfold
decrease.
Decimal Units and Values
Terminology
place value
the location of a numeral in a
string of numbers that describes
the numeral’s relationship to the
decimal point
Terminology
leading zero
a zero that is placed to the left of
the decimal point, in the ones
place, in a number that is less
than zero and is being
represented by a decimal value
Decimals
• A decimal is a fraction in which the
denominator is 10 or some multiple of 10.
• Numbers written to the right of decimal
point < 1.
• Numbers written to the left of the decimal
point > 1
Example 2
Multiply the two given fractions.
Terminology
decimal
a fraction value in which the
denominator is 10 or some
multiple of 10
Remember
• Numbers to the left of the decimal point are
whole numbers.
• Numbers to the right of the decimal point
are decimal fractions (part of a whole).
Decimal Places
Decimals
Adding or Subtracting Decimals
• Place the numbers in columns so that the
decimal points are aligned directly under
each other.
• Add or subtract from the right column to the
left column.
Decimals
Multiplying Decimals
• Multiply two decimals as whole numbers.
• Add the total number of decimal places that
are in the two numbers being multiplied.
• Count that number of places from right to
left in the answer, and insert a decimal
point.
Decimals
Dividing Decimals
1. Change both the divisor and dividend to whole numbers
by moving their decimal points the same number of places
to the right.
• divisor: number doing the dividing, the denominator
• dividend: number being divided, the numerator
2. If the divisor and the dividend have different number of
digits after the decimal point, choose the one that has
more digits and move its decimal point a sufficient
number of places to make it a whole number.
Decimals
Dividing Decimals
3. Move the decimal point in the other number the same
number of places, adding zeros at the end if necessary.
4. Move the decimal point in the dividend the same number
of places, adding a zero at the end.
Decimals
Dividing Decimals
1.45 ÷ 3.625 = 0.4
1.45 1450

 0 .4
3.625 3625
Decimals
Rounding Decimals
• Rounding numbers is essential for accuracy.
• It may not be possible to measure a very small
quantity such as a hundredth of a milliliter.
• A volumetric dose is commonly rounded to the
nearest tenth.
• A solid dose is commonly rounded to the
hundredth or thousandth place, pending the
accuracy of the measuring device.
Decimals
Rounding to the Nearest Tenth
1. Carry the division out to the hundredth place
2. If the hundredth place number ≥ 5, + 1 to the
tenth place
3. If the hundredth place number ≤ 5, round the
number down by omitting the digit in the
hundredth place
5.65 becomes 5.7 4.24 becomes 4.2
Decimals
Rounding to the Nearest Hundredth or
Thousandth Place
3.8421 = 3.84
41.2674 = 41.27
0.3928 = 0.393
4.1111 = 4.111
Decimals
Rounding the exact dose 0.08752 g
. . . to the nearest tenth: 0.1 g
. . . to he nearest hundredth: 0.09 g
. . . to the nearest thousandth: 0.088 g
Discussion
When a number that has been rounded to
the tenth place is multiplied or divided by a
number that was rounded to the hundredth
or thousandth place, the resultant answer
must be rounded back to the tenth place.
Why?
Discussion
When a number that has been rounded to
the tenth place is multiplied or divided by a
number that was rounded to the hundredth
or thousandth place, the resultant answer
must be rounded back to the tenth place.
Why?
Answer: The answer can only be accurate
to the place to which the highest rounding
was made in the original numbers.
Decimals
• In most cases, a zero occurring at the end of
a digits is not written.
• Do not drop the zero when the last digit
resulting from rounding is a zero. Such a
zero is considered significant to that
particular problem or dosage.
Numerical Ratios
Ratios represent the relationship between
• two parts of the whole
• one part to the whole
Numerical Ratios
Written with as follows:
1:2
3:4
“1 part to 2 parts”
“3 parts to 4 parts”
½
¾
Can use “per,” “in,” or “of,” instead of “to”
Terminology
ratio
a numerical representation of the
relationship between two parts
of the whole or between one part
and the whole
Numerical Ratios in the
Pharmacy
1:100 concentration of a drug means . . .
Numerical Ratios in the
Pharmacy
1:100 concentration of a drug means . . .
. . . there is 1 part drug in 100 parts solution
Proportions
• An expression of equality between two
ratios.
• Noted by :: or =
3:4 = 15:20
or
3:4 :: 15:20
Terminology
proportion
an expression of equality
between two ratios
Proportions
If a proportion is true . . .
product of means = product of extremes
3:4 = 15:20
3 × 20 = 4 × 15
60
= 60
Proportions
product of means = product of extremes
a:b = c:d
b×c=a×d
Proportions in the Pharmacy
• Proportions are frequently used to
calculate drug doses in the pharmacy.
• Use the ratio-proportion method any time
one ratio is complete and the other is
missing a component.
Terminology
ratio-proportion
method
a conversion method based on
comparing a complete ratio to a
ratio with a missing component
Rules for Ratio-Proportion
Method
• Three of the four amounts must be
known.
• The numerators must have the same unit
of measure.
• The denominators must have the same
unit of measure.
Steps for solving for x
1. Calculate the proportion by placing the ratios
in fraction form so that the x is in the upperleft corner.
Steps for solving for x
1. Calculate the proportion by placing the ratios in
fraction form so that the x is in the upper-left corner.
2. Check that the unit of measurement in the
numerators is the same and the unit of
measurement in the denominators is the
same.
Steps for solving for x
1. Calculate the proportion by placing the ratios in
fraction form so that the x is in the upper-left corner.
2. Check that the unit of measurement in the numerators
is the same and the unit of measurement in the
denominators is the same.
3. Solve for x by multiplying both sides of the
proportion by the denominator of the ratio
containing the unknown, and cancel.
Steps for solving for x
1. Calculate the proportion by placing the ratios in
fraction form so that the x is in the upper-left corner.
2. Check that the unit of measurement in the numerators
is the same and the unit of measurement in the
denominators is the same.
3. Solve for x by multiplying both sides of the proportion
by the denominator of the ratio containing the
unknown, and cancel.
4. Check your answer by seeing if the product
of the means equals the product of the
extremes.
Remember
When setting up a proportion to solve a
conversion, the units in the numerators
must match, and the units in the
denominators must match.
Example 3
Solve for x.
Example 3
Solve for x.
Example 3
Solve for x.
Percents
• Percent means “per 100” or hundredths.
• Represented by symbol %
30% = 30 parts in total of 100 parts,
30
30:100, 0.30, or
100
Terminology
percent
the number of parts per 100; can
be written as a fraction, a
decimal, or a ratio
Discussion
If you take a test with 100 questions,
and you get a score of 89%, how
many questions did you get correct?
Discussion
If you take a test with 100 questions,
and you get a score of 89%, how
many questions did you get correct?
Answer: 89
89:100, 89/100, or 0.89
Percents in the Pharmacy
• Percent strengths are used to describe IV
solutions and topically applied drugs.
• The higher the % of dissolved
substances, the greater the strength.
Percents in the Pharmacy
A 1% solution contains . . .
• 1 g of drug per 100 mL of fluid
• Expressed as 1:100, 1/100, or 0.01
Percents in the Pharmacy
A 1% hydrocortisone cream contains . . .
• 1 g of hydrocortisone per 100 g of cream
• Expressed as 1:100, 1/100, or 0.01
Safety Note!
The higher the percentage of a dissolved
substance, the greater the strength.
Percents in the Pharmacy
• Multiply the first number in the ratio (the
solute) while keeping the second number
unchanged, you increase the strength.
• Divide the first number in the ration
while keeping the second number
unchanged, you decrease the strength.
Equivalent Values
Percent
Fraction
Decimal
Ratio
45%
45
100
0.45
45:100
0.5%
0.5
100
0.005
0.5:100
Converting a Ratio to a Percent
1. Designate the first number of the ratio as
the numerator and the second number as
the denominator.
2. Multiply the fraction by 100%, and
simply as needed.
Remember
Multiplying a number or a fraction
by 100% does not change the
value.
Converting a Ratio to a Percent
5:1 = 5/1 × 100% = 5 × 100% = 500%
1:5 = 1/5 × 100% = 100%/5 = 20%
1:2 = 1/2 × 100% = 100%/2 = 50%
Converting a Percent to a Ratio
1. Change the percent to a fraction by
dividing it by 100.
Converting a Percent to a Ratio
1. Change the percent to a fraction by
dividing it by 100.
2. Reduce the fraction to its lowest
terms.
Converting a Percent to a Ratio
1. Change the percent to a fraction by
dividing it by 100.
2. Reduce the fraction to its lowest terms.
3. Express this as a ratio by making the
numerator the first number of the
ratio and the denominator the second
number.
Converting a Percent to a Ratio
2% = 2 ÷ 100 = 2/100 = 1/50 = 1:50
10% = 10 ÷ 100 = 10/100 = 1/10 = 1:10
75% = 75 ÷ 100 = 75/100 = 3/4 = 3:4
Converting a Percent to a
Decimal
1. Divide by 100% or insert a decimal
point two places to the left of the last
number, inserting zeros if necessary.
2. Drop the % symbol.
Remember
Multiplying or dividing by 100%
does not change the value because
100% = 1.
Converting a Decimal to a
Percent
1. Multiply by 100% or insert a decimal
point two places to the right of the last
number, inserting zeros if necessary.
2. Add the the % symbol.
Percent to Decimal
4% = 0.04
4 ÷ 100% = 0.04
15% = 0.15
15 ÷ 100% = 0.15
200% = 2
200 ÷ 100% = 2
Decimal to Percent
0.25 = 25%
0.25 × 100% = 25%
1.35 = 135%
1.35 × 100% = 135%
0.015 = 1.5%
0.015 × 100% = 1.5%
Terms to Remember
• common denominator
• least common denominator
• decimal
• leading zero
• ratio
• proportion
• percent
COMMON CALCULATIONS IN
THE PHARMACY
• Converting Quantities between the Metric and
Common Measure Systems
• Calculations of Doses
• Preparation of Solutions
COMMON CALCULATIONS IN
THE PHARMACY
• Converting Quantities between the Metric and
Common Measure Systems
Example 4
How many milliliters are there in
1 gal, 12 fl oz?
According to the values in Table 5.7, 3840 mL
are found in 1 gal. Because 1 fl oz contains 30
mL, you can use the ratio-proportion method
to calculate the amount of milliliters in 12 fl
oz as follows:
Example 4
How many milliliters are there in
1 gal, 12 fl oz?
Example 4
How many milliliters are there in
1 gal, 12 fl oz?
Example 4
How many milliliters are there in
1 gal, 12 fl oz?
Example 5
A solution is to be used to fill hypodermic
syringes, each containing 60 mL, and 3 L of
the solution is available. How many
hypodermic syringes can be filled with the 3 L
of solution?
From Table 5.2, 1 L is 1000 mL. The available
supply of solution is therefore
Example 5
How many hypodermic syringes can be filled
with the 3 L of solution?
Determine the number of syringes by
using the ratio-proportion method:
Example 5
How many hypodermic syringes can be filled
with the 3 L of solution?
Example 5
How many hypodermic syringes can be filled
with the 3 L of solution?
Example 6
You are to dispense 300 mL of a liquid
preparation. If the dose is 2 tsp, how
many doses will there be in the final
preparation?
Begin solving this problem by converting
to a common unit of measure using
conversion values in Table 5.7.
Example 6
If the dose is 2 tsp, how many doses will
there be in the final preparation?
Using these converted measurements, the
solution can be determined one of two ways.
Solution 1: Using the ratio proportion method
and the metric system,
Example 6
If the dose is 2 tsp, how many doses will
there be in the final preparation?
Example 6
If the dose is 2 tsp, how many doses will
there be in the final preparation?
Example 7
How many grains of acetaminophen
should be used in a Rx for 400 mg
acetaminophen?
Solve this problem by using the ratio-proportion
method. The unknown number of grains and the
requested number of milligrams go on the left side,
and the ratio of 1 gr 65 mg goes on the right side,
per Table 5.5.
Example 7
How many grains of acetaminophen
should be used in the prescription?
Example 7
How many grains of acetaminophen
should be used in the prescription?
Example 8
A physician wants a patient to be given 0.8
mg of nitroglycerin. On hand are tablets
containing nitroglycerin 1/150 gr. How
many tablets should the patient be given?
Begin solving this problem by determining
the number of grains in a dose by setting up
a proportion and solving for the unknown.
Example 8
How many tablets should the patient
be given?
Example 8
How many tablets should the patient
be given?
Example 8
How many tablets should the patient
be given?
Example 8
How many tablets should the patient
be given?
Example 8
How many tablets should the patient
be given?
COMMON CALCULATIONS IN
THE PHARMACY
• Calculations of Doses
active ingredient (to be administered)/solution
(needed)
=
active ingredient (available)/solution (available
Measurement and Calculation Issues
Safety Note!
Always double-check the units
in a proportion and doublecheck your calculations.
Example 9
You have a stock solution that contains 10
mg of active ingredient per 5 mL of
solution. The physician orders a dose of 4
mg. How many milliliters of the stock
solution will have to be administered?
Example 9
How many milliliters of the stock
solution will have to be administered?
Example 9
How many milliliters of the stock
solution will have to be administered?
Example 10
An order calls for Demerol 75 mg IM
q4h prn pain. The supply available is in
Demerol 100 mg/mL syringes. How many
milliliters will the nurse give for one
injection?
Example 10
How many milliliters will the nurse give
for one injection?
Example 10
How many milliliters will the nurse give
for one injection?
Example 11
An average adult has a BSA of 1.72 m2
and requires an adult dose of 12 mg of a
given medication. If the child has a BSA
of 0.60 m2, and if the proper dose for
pediatric and adult patients is a linear
function of the BSA, what is the proper
pediatric dose?
Round off the final answer.
Example 11
What is the proper pediatric
dose?
Example 11
What is the proper pediatric
dose?
Example 11
What is the proper pediatric
dose?
Example 11
What is the proper pediatric
dose?
COMMON CALCULATIONS IN
THE PHARMACY
• Preparation of Solutions
powder volume =
final volume – diluent volume
Example 12
A dry powder antibiotic must be
reconstituted for use. The label states
that the dry powder occupies 0.5 mL.
Using the formula for solving for powder
volume, determine the diluent volume
(the amount of solvent added). You are
given the final volume for three different
examples with the same powder volume.
Example 12
Using the formula for solving for
powder volume, determine the
diluent volume.
Example 12
Using the formula for solving for
powder volume, determine the
diluent volume.
Example 13
You are to reconstitute 1 g of dry
powder. The label states that you
are to add 9.3 mL of diluent to
make a final solution of 100
mg/mL. What is the powder
volume?
Example 13
What is the powder volume?
Step 1. Calculate the final volume. The
strength of the final solution will be 100
mg/mL.
Example 13
What is the powder volume?
Example 13
What is the powder volume?
Example 13
What is the powder volume?
Measurement and Calculation Issues
Safety Note!
An injected dose generally has
a volume greater than 0.1 mL
and less than 1 mL.
Example 14
Dexamethasone is available as a 4
mg/mL preparation; an infant is to
receive 0.35 mg. Prepare a dilution
so that the final concentration is 1
mg/mL. How much diluent will you
need if the original product is in a 1
mL vial and you dilute the entire
vial?
Example 14
How much diluent will you need if
the original product is in a 1 mL vial
and you dilute the entire vial?
Example 14
How much diluent will you need if
the original product is in a 1 mL vial
and you dilute the entire vial?
Example 14
How much diluent will you need if
the original product is in a 1 mL vial
and you dilute the entire vial?
Example 15
Prepare 250 mL of dextrose 7.5%
weight in volume (w/v) using
dextrose 5% (D5W) w/v and
dextrose 50% (D50W) w/v. How
many milliliters of each will be
needed?
Example 15
How many milliliters of each will
be needed?
Step 1. Set up a box arrangement and at the
upper-left corner, write the percent of the highest
concentration (50%) as a whole number.
Example 15
How many milliliters of each will
be needed?
Step 2. Subtract the center number from the
upper-left number (i.e., the smaller from the
larger) and put it at the lower-right corner.
Now subtract the lower-left number from the
center number (i.e., the smaller from the
larger), and put it at the upper-right corner.
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Example 15
How many milliliters of each will
be needed?
Terms to Remember
• power volume (pv)
• alligation
Discussion
Visit www.malpracticeweb.com, and look
under Miscellaneous to find legal summaries
of the following cases. Describe the decision
and explain how this decision affects
pharmacy technicians.
a. J.C. vs. Osco Drug
b. P.H. vs. Osco Drug
Discussion
What activities of the pharmacy
technician require skill in calculations?