Basic Pharmaceutical Measurements and Calculations

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Chapter 5
Basic Pharmaceutical Measurements and
Calculations
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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.

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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.

Edited by Dr. Ryan Lambert-Bellacov, chiropractor
for Back in the Game in West Linn, OR
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• Back in the Game Sports Medicine is a clinic
  dedicated to the treatment of physical injuries
  to the body. Caring for an injured body involves
  more than making the diagnosis it's about
  understanding and treating the cause to prevent
  future injuries. The clinic addresses variety of
  injuries to the body whether it be from a car
  accident to over-use trauma. When injuries occur,
  it is no longer enough for people to "take it
  easy for awhile" or "work through it."
• PHYSICIAL THERAPYWe believe that the true goal
  of physical therapy involves restoration of
  function through neuromuscular re-education and
  specialized manual techniques. These techniques
  restore movement, balance and quality of life. At
  Back in the Game, we go a step further and
  instruct people how to keep their bodies stronger
  and healthier. We do this by teaching proper body
  mechanics and developing personalized exercises
  that will help prevent re-injury.
• At Back In The Game, it's all about you. You're
  the reason we're here. The entire visit is
  centered around giving you an experience uncommon
  in today's impersonal medical world. We recognize
  that you are a unique human being with specific
  needs which require talented people who truly
  care and we strive to deliver this care in a
  professional, yet comfortable environment. Dr.
  Lambert, a state licensed Chiropractic Physician,
  who has training in sports medicine, heads Back
  In The Game.

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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.

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SYSTEMS OF PHARMACEUTICAL MEASUREMENT

• Metric System
• Common Measures
• Numeral Systems

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BASIC MATHEMATICS USED IN PHARMACY PRACTICE

• Fractions
• Decimals
• Ratios and Proportions

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COMMON CALCULATIONS IN THE PHARMACY

• Converting Quantities between the Metric and
  Common Measure Systems
• Calculations of Doses
• Preparation of Solutions

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SYSTEMS OF PHARMACEUTICAL MEASUREMENT

• Metric System
• Common Measures
• Numeral Systems

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Measurements in the Metric System

• (a) Distance or length
• (b) Area
• (c) Volume

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Système International Prefixes
Table 5.1
Prefix Meaning
micro- one millionth (basic unit 106, or unit 0.000,001)
milli- one thousandth (basic unit 103, or unit 0.001)
centi- one hundredth (basic unit 102, or unit 0.01)
deci- one tenth (basic unit 101, or unit 0.1)
hecto- one hundred times (basic unit 102, or unit 100)
kilo- one thousand times (basic unit 103, or unit 1000)
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Common Metric Units Weight
Table 5.2
Basic Unit Equivalent
1 gram (g) 1000 milligrams (mg)
1 milligram (mg) 1000 micrograms (mcg), one thousandth of a gram (g)
1 kilogram (kg) 1000 grams (g)
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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)
1 millimeter (mm) 0.001 m 1000 micrometers or microns (mcm)
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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)
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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.
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Common Metric Conversions
Table 5.3
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
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Common Metric Conversions
Table 5.3
Conversion Instruction Example
liters (L) to milliliters (mL) multiply by 1000 (move decimal point three places to the right) 2.5 L 2500 mL
milliliters (mL) to liters (L) multiply by 0.001 (move decimal point three places to the left) 238 mL 0.238 L
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Apothecary Symbols
Table 5.4
Volume Volume Weight Weight
Unit of measure Symbol Unit of measure Symbol Unit of measure Symbol
minim ? grain gr
fluidram fZ scruple ?
fluidounce f ? dram Z
pint pt ounce ?
quart qt pound ? or
gallon gal
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Apothecary System Volume
Table 5.5
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.
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Apothecary System Weight
Table 5.5
Measurement Unit Equivalent within System Metric Equivalent
1 gr 65 mg
15.432 gr 1 g
1 ? 20 gr 1.3 g
1 Z 3 ? or 60 gr 3.9 g
1 ? 8 Z or 480 gr 30 g (31.1 g)
1 12 ?or 5760 gr 373.2 g
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Measurement and Calculation Issues
Safety Note!
For safety reasons, the use of the apothecary
system is discouraged. Use the metric system
instead.
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Avoirdupois System
Table 5.6
Measurement Unit Equivalent within System Metric Equivalent
1 gr (grain) 65 mg
1 oz (ounce) 437.5 gr 30 g (28.35 g)
1 lb (pound) 16 oz or 7000 gr 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).

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Household Measure Volume
Table 5.7
Measurement Unit Equivalent within System Metric Equivalent
1 tsp (teaspoonful) 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.

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Household Measure Weight
Table 5.7
Measurement Unit Equivalent within System Metric Equivalent
1 oz (ounce) 30 g
1 lb (pound) 16 oz 454 g
2.2 lb 1 kg
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Measurement and Calculation Issues
Safety Note!
New safety guidelines are discouraging use of
Roman numerals.
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Comparison of Roman and Arabic Numerals
Table 5.8
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
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Terms to Remember

metric system meter gram liter
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BASIC MATHEMATICS USED IN PHARMACY PRACTICE

• Fractions
• Decimals
• Ratios and Proportions

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Fractions

• When something is divided into parts, each part
  is considered a fraction of the whole.

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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).

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Fractions of the Whole Pie
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Fractions

• If we have a 1000 mg tablet,
• ½ tablet 500 mg
• ¼ tablet 250 mg

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Terminology
fraction
a portion of a whole that is represented as a
ratio
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Fractions
Fractions have two parts,
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Fractions

• Fractions have two parts,
• Numerator (the top part)

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Fractions

• Fractions have two parts,
• Numerator (the top part)
• Denominator (the bottom part)

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Terminology
numerator
the number on the upper part of a fraction
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Terminology
denominator
the number on the bottom part of a fraction
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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.
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Discussion

• What are the distinguishing characteristics of
  the following?
• proper fraction
• improper fraction
• mixed number

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Remember
The symbol gt means is greater than. The
symbol gt means is less than.
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Terminology
proper fraction

• a fraction with a value of less than 1
• a fraction with a numerator value smaller than
  the denominators value

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Terminology
improper fraction

• a fraction with a value of larger than 1
• a fraction with a numerator value larger than the
  denominators value

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Terminology
mixed number
a whole number and a fraction
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Adding or Subtracting Fractions

• When adding or subtracting fractions with unlike
  denominators, it is necessary to create a common
  denominator.

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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.

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Terminology
common denominator
a number into which each of the unlike
denominators of two or more fractions can be
divided evenly
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Remember
Multiplying a number by 1 does not change the
value of the number. 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.
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Guidelines for Finding a Common Denominator

• Examine each denominator in the given fractions
  for its divisors, or factors.

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Guidelines for Finding a Common Denominator

• Examine each denominator in the given fractions
  for its divisors, or factors.
• See what factors any of the denominators have in
  common.

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Guidelines for Finding a Common Denominator

• Examine each denominator in the given fractions
  for its divisors, or factors.
• See what factors any of the denominators have in
  common.
• 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.

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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.
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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.
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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.
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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.
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Example 1 Find the least common denominator of
the following fractions
The following are two equivalent fractions
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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.
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Multiplying Fractions
When multiply fractions, multiply the numerators
by numerators and denominators by denominators.
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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.
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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.
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Discussion
What happens to the value of a fraction when you
multiply the numerator by a number?
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Discussion
What happens to the value of a fraction when you
multiply the numerator by a number? Answer The
value of the fraction increases.
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Discussion
What happens to the value of a fraction when you
multiply the denominator by a number?
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Discussion
What happens to the value of a fraction when you
multiply the denominator by a number? Answer
The value of the fraction decreases.
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Discussion
What happens to the value of a fraction when you
multiply the numerator and denominator by the
same number?
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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.
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Multiplying Fractions
Dividing the denominator by a number is the same
as multiplying the numerator by that number.
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Multiplying Fractions
Dividing the numerator by a number is the same as
multiplying the denominator by that number.
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Dividing Fractions
To divide by a fraction, multiply by its
reciprocal, and then reduce it if necessary.
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Terms to Remember

fraction numerator denominator proper fraction improper fraction mixed number
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The Arabic System
The Arabic system is also called the decimal
system.
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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.
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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.

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Decimal Units and Values
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Terminology
place value
the location of a numeral in a string of numbers
that describes the numerals relationship to the
decimal point
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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
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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 lt
  1.
• Numbers written to the left of the decimal point
  gt 1

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Example 2 Multiply the two given fractions.
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Terminology
decimal
a fraction value in which the denominator is 10
or some multiple of 10
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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).

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Decimal Places
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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.

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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.

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Decimals

• Dividing Decimals
• 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
• 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.

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Decimals

• Dividing Decimals
• 3. Move the decimal point in the other number the
  same number of places, adding zeros at the end if
  necessary.
• Move the decimal point in the dividend the same
  number of places, adding a zero at the end.

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Decimals
Dividing Decimals 1.45 3.625 0.4
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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.

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Decimals

• Rounding to the Nearest Tenth
• Carry the division out to the hundredth place
• If the hundredth place number 5, 1 to the
  tenth place
• 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

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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
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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
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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?
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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.
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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.

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Numerical Ratios

• Ratios represent the relationship between
• two parts of the whole
• one part to the whole

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Numerical Ratios

• Written with as follows
• 12 1 part to 2 parts ½
• 34 3 parts to 4 parts ¾
• Can use per, in, or of, instead of to

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Terminology
ratio
a numerical representation of the relationship
between two parts of the whole or between one
part and the whole
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Numerical Ratios in the Pharmacy
1100 concentration of a drug means . . .
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Numerical Ratios in the Pharmacy
1100 concentration of a drug means . . . . . .
there is 1 part drug in 100 parts solution
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Proportions

• An expression of equality between two ratios.
• Noted by or
• 34 1520 or 34 1520

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Terminology
proportion
an expression of equality between two ratios
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Proportions
If a proportion is true . . . product of means
product of extremes 34 1520 3 20
4 15 60 60
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Proportions
product of means product of extremes
ab cd b c a d
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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.

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Terminology
ratio-proportion method
a conversion method based on comparing a complete
ratio to a ratio with a missing component
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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.

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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.

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108
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.

109
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.

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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.

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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.
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Example 3 Solve for x.
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Example 3 Solve for x.
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Example 3 Solve for x.
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Percents

• Percent means per 100 or hundredths.
• Represented by symbol
• 30 30 parts in total of 100 parts,
• 30100, 0.30, or

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Terminology
percent
the number of parts per 100 can be written as a
fraction, a decimal, or a ratio
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Discussion
If you take a test with 100 questions, and you
get a score of 89, how many questions did you
get correct?
118
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 89100, 89/100, or
0.89
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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.

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Percents in the Pharmacy

• A 1 solution contains . . .
• 1 g of drug per 100 mL of fluid
• Expressed as 1100, 1/100, or 0.01

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Percents in the Pharmacy

• A 1 hydrocortisone cream contains . . .
• 1 g of hydrocortisone per 100 g of cream
• Expressed as 1100, 1/100, or 0.01

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Safety Note!
The higher the percentage of a dissolved
substance, the greater the strength.
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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.

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Equivalent Values
Percent Fraction Decimal Ratio
45 0.45 45100
0.5 0.005 0.5100
125
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.

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Remember
Multiplying a number or a fraction by 100 does
not change the value.
127
Converting a Ratio to a Percent
51 5/1 100 5 100 500 15 1/5
100 100/5 20 12 1/2 100 100/2
50
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Converting a Percent to a Ratio

1. Change the percent to a fraction by dividing it
   by 100.

129
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.

130
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.

131
Converting a Percent to a Ratio
2 2 100 2/100 1/50 150 10 10 100
10/100 1/10 110 75 75 100 75/100
3/4 34
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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.

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Remember
Multiplying or dividing by 100 does not change
the value because 100 1.
134
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.

135
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
136
Terms to Remember

common denominator least common denominator decimal leading zero ratio proportion percent
137
COMMON CALCULATIONS IN THE PHARMACY

• Converting Quantities between the Metric and
  Common Measure Systems
• Calculations of Doses
• Preparation of Solutions

Edited by Dr. Ryan Lambert-Bellacov, chiropractor
for Back in the Game in West Linn, OR
138
COMMON CALCULATIONS IN THE PHARMACY

• Converting Quantities between the Metric and
  Common Measure Systems

139
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
140
Example 4 How many milliliters are there in 1
gal, 12 fl oz?
141
Example 4 How many milliliters are there in 1
gal, 12 fl oz?
142
Example 4 How many milliliters are there in 1
gal, 12 fl oz?
143
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
144
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
145
Example 5 How many hypodermic syringes can be
filled with the 3 L of solution?
146
Example 5How many hypodermic syringes can be
filled with the 3 L of solution?
147
Example 6You 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.
148
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,
149
Example 6 If the dose is 2 tsp, how many doses
will there be in the final preparation?
150
Example 6 If the dose is 2 tsp, how many doses
will there be in the final preparation?
151
Example 7How many grains of acetaminophenshould
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.
152
Example 7How many grains of acetaminophenshould
be used in the prescription?
153
Example 7 How many grains of acetaminophenshould
be used in the prescription?
154
Example 8A 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.
155
Example 8 How many tablets should the patient be
given?
156
Example 8How many tablets should the patient be
given?
157
Example 8How many tablets should the patient be
given?
158
Example 8How many tablets should the patient be
given?
159
Example 8How many tablets should the patient be
given?
160
COMMON CALCULATIONS IN THE PHARMACY

• Calculations of Doses

active ingredient (to be administered)/solution
(needed) active ingredient (available)/solutio
n (available
161
Measurement and Calculation Issues
Safety Note!
Always double-check the units in a proportion and
double-check your calculations.
162
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?
163
Example 9How many milliliters of the stock
solution will have to be administered?
164
Example 9 How many milliliters of the stock
solution will have to be administered?
165
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?
166
Example 10 How many milliliters will the nurse
give for one injection?
167
Example 10 How many milliliters will the nurse
give for one injection?
168
Example 11An 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.
169
Example 11 What is the proper pediatric dose?
170
Example 11What is the proper pediatric dose?
171
Example 11 What is the proper pediatric dose?
172
Example 11What is the proper pediatric dose?
173
COMMON CALCULATIONS IN THE PHARMACY

• Preparation of Solutions

powder volume final volume diluent volume
174
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.
175
Example 12 Using the formula for solving for
powder volume, determine the diluent volume.
176
Example 12 Using the formula for solving for
powder volume, determine the diluent volume.
177
Example 13You 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?
178
Example 13 What is the powder volume?
Step 1. Calculate the final volume. The strength
of the final solution will be 100 mg/mL.
179
Example 13 What is the powder volume?
180
Example 13 What is the powder volume?
181
Example 13What is the powder volume?
182
Measurement and Calculation Issues
Safety Note!
An injected dose generally has a volume greater
than 0.1 mL and less than 1 mL.
183
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?
184
Example 14 How much diluent will you need if the
original product is in a 1 mL vial and you dilute
the entire vial?
185
Example 14How much diluent will you need if the
original product is in a 1 mL vial and you dilute
the entire vial?
186
Example 14 How much diluent will you need if the
original product is in a 1 mL vial and you dilute
the entire vial?
187
Example 15Prepare 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?
188
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.
189
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.
190
Example 15 How many milliliters of each will be
needed?
191
Example 15 How many milliliters of each will be
needed?
192
Example 15 How many milliliters of each will be
needed?
193
Example 15 How many milliliters of each will be
needed?
194
Example 15 How many milliliters of each will be
needed?
195
Example 15 How many milliliters of each will be
needed?
Edited by Dr. Ryan Lambert-Bellacov, chiropractor
for Back in the Game in West Linn, OR
196
Example 15How many milliliters of each will be
needed?
197
Example 15 How many milliliters of each will be
needed?
198
Example 15 How many milliliters of each will be
needed?
199
Example 15 How many milliliters of each will be
needed?
200
Example 15 How many milliliters of each will be
needed?
201
Terms to Remember

power volume (pv) alligation
Edited by Dr. Ryan Lambert-Bellacov, chiropractor
for Back in the Game in West Linn, OR
202
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
203
Discussion
What activities of the pharmacy technician
require skill in calculations?
204

• Back in the Game Sports Medicine is a clinic
  dedicated to the treatment of physical injuries
  to the body. Caring for an injured body involves
  more than making the diagnosis it's about
  understanding and treating the cause to prevent
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  easy for awhile" or "work through it."
• PHYSICIAL THERAPYWe believe that the true goal
  of physical therapy involves restoration of
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  restore movement, balance and quality of life. At
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  instruct people how to keep their bodies stronger
  and healthier. We do this by teaching proper body
  mechanics and developing personalized exercises
  that will help prevent re-injury.
• At Back In The Game, it's all about you. You're
  the reason we're here. The entire visit is
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  in today's impersonal medical world. We recognize
  that you are a unique human being with specific
  needs which require talented people who truly
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  professional, yet comfortable environment. Dr.
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  who has training in sports medicine, heads Back
  In The Game.