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Chapter 3

Measurement Systems and

Conversion Procedures

Objectives

▪

▪

▪

▪

Interpret the systems of measurement

Simplify units using dimensional analysis

Perform metric system conversions

Perform conversions between metric and

nonmetric systems

© 2010 Delmar, Cengage Learning.

2

Objectives (cont’d.)

▪ Perform conversions between apothecary

and household systems

▪ Perform temperature conversions between

Celsius, Fahrenheit and Kelvin

© 2010 Delmar, Cengage Learning.

3

Systems of Measurement

▪ United States Customary System of

Measurement:

• Distance:

– 1 ft = 12 in

– 1 yd = 3 ft

– 1 mi = 5280 ft

• Volume:

– 8 fl oz = 1 cup

– 1 pt = 2 cups

– 1 qt = 2 pt

– 4 qt = 1 gal

© 2010 Delmar, Cengage Learning.

4

Systems of Measurement (cont’d.)

▪ Metric system:

• m → meter → Length

• l or L → liter → Volume

• g → gram → Weight

– 0.91 m = 1 yd

– 3.79 L = 1 gal

– 28.3 g = 1 oz

© 2010 Delmar, Cengage Learning.

5

Systems of Measurement (cont’d.)

Table 3.1

Metric Prefixes

and Values

© 2010 Delmar, Cengage Learning.

6

Basic Dimensional Analysis

▪ Algebraically changing or converting units

of measure

• .

• .

• Grams per liter

© 2010 Delmar, Cengage Learning.

7

Conversions Within the Metric Systems

▪ Horizontal format:

1. Identify decimal location in the number being

converted

2. Identify prefix location on horizontal diagram

3. Find the difference between the two exponents

associated with each prefix

© 2010 Delmar, Cengage Learning.

8

Conversions Within the Metric Systems

(cont’d.)

▪ Horizontal format:

4. Conversion is moving right on the diagram:

– Move decimal to the right by the amount calculated

in step 3

5. Conversion is moving left on the diagram:

– Move the decimal to the left by the amount

calculated in step 3

Figure 3.1 Horizontal format for metric prefixes and values

© 2010 Delmar, Cengage Learning.

9

Conversions Within the Metric Systems

(cont’d.)

▪ Horizontal format: (cont’d.)

• Convert 12 mL to microliters

– Identify decimal: 12.0

– Identify prefixes in diagram

– Difference is -3 –(-6) = 3

– 12 mL = 12,000 μL

© 2010 Delmar, Cengage Learning.

10

Conversions Within the Metric Systems

(cont’d.)

▪ Dimensional analysis:

• 1 will always be placed with two-letter unit

▪ Convert: 12μL to mL

• .

© 2010 Delmar, Cengage Learning.

11

Conversions Between Metric and

Nonmetric

Table 3.2 Relationships between the U.S. System and the Metric

System

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12

Conversions Between Metric and

Nonmetric (cont’d.)

▪ Convert 5 kg to oz:

• Convert kg to lbs

• Convert lbs to oz

© 2010 Delmar, Cengage Learning.

13

Apothecary Systems

▪ Apothecary equivalents:

•

•

•

•

•

•

•

•

1 fl oz = 8 fl dr

4 mL = 1 fl dr

60 minims = 1 fl dr

1 g = 15 gr

1 gr = 60 mg

1 mL = 16 minims

1 pt = 16 fl oz

1 qt = 2 pt

© 2010 Delmar, Cengage Learning.

14

Apothecary Systems (cont’d.)

▪ 50mg is how many grains?

• .

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15

Apothecary Systems (cont’d.)

▪ 250 fl dr equals how many milliliters?

• .

© 2010 Delmar, Cengage Learning.

16

Household Systems

▪ Household equivalents:

•

•

•

•

•

•

•

•

60 drops (gtt) = 1 tsp

1 fl oz = 30 mL

2 tbs = 1 oz

6 fl oz = 1 teacup

8 fl oz = 1 glass

16 oz = 1 lb

1 cup = 8 fl oz

5 mL = 1 tsp

© 2010 Delmar, Cengage Learning.

17

Household Systems (cont’d.)

▪ You drank 3 ½ glasses of water

• How many ounces did you consume?

• .

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18

Household Systems (cont’d.)

▪ How many tablespoons are in 12oz?

• .

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19

Household, Apothecary, and Metric

Equivalents

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20

Temperature Conversions

▪ Three scales to measure temperature:

• Fahrenheit

• Celsius

• Kelvin

▪ Converting Celsius to Fahrenheit:

• .

or

© 2010 Delmar, Cengage Learning.

21

Temperature Conversions (cont’d.)

▪ 0°C equals how many °F?

• °F = (0° × 1.8) + 32°= 0° + 32° = 32°

▪ 75°F equals how many °C?

• .

© 2010 Delmar, Cengage Learning.

22

Temperature Conversions (cont’d.)

▪ Converting Celsius to Kelvin:

• K = °C + 273.15

• 100°C

K = 100° + 273.15° = 373.15°

• Converting Kelvin to Fahrenheit:

• °F = 1.8K − 459.67°

• 300K

°F = 1.8(300°) − 459.67° = 80.33°

© 2010 Delmar, Cengage Learning.

23

Summary

▪ To perform metric conversions, we must

be familiar with Table 3.1

▪ Conversions within the metric system can

be done using the horizontal format

▪ Apothecary system: used in calculating

drug dosages

▪ Household system: used when

administering medications in the home

© 2010 Delmar, Cengage Learning.

24

Summary (cont’d.)

▪ The three main temperature formulas:

© 2010 Delmar, Cengage Learning.

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Chapter 4

Dilutions, Solutions, and

Concentrations

Objectives

▪

▪

▪

▪

Perform dilutions

Determine concentrations

Solve dilution problems

Solve problems involving percents

© 2010 Delmar, Cengage Learning.

2

Dilutions

▪ It is common to dilute solutions with water

or saline

• Formula relating the two volumes and two

concentrations:

▪ When preparing solutions:

• One is constantly mixing a concentrated

solution (concentrate) with a solvent (diluent)

– Decreases concentration

© 2010 Delmar, Cengage Learning.

3

Dilutions (cont’d.)

▪ Parts concentrate + parts diluent = total

volume

• Solution contains 1 μL serum and 6 μL saline

– Ratio 1:6

– Ratio of serum to total volume would be 1:7

– Ratio of saline to total volume would be 6:7

– Dilutions represent parts of concentrate in total

volume (1:7)

© 2010 Delmar, Cengage Learning.

4

Dilutions (cont’d.)

▪ Make a 1 in 9 dilution of insulin in water

• Total volume must be 225 mL

▪ What volume of insulin is needed?

• Cross multiplying gives: 9x = 225

• x = 25

• 25 μL insulin is needed

© 2010 Delmar, Cengage Learning.

5

Dilutions (cont’d.)

▪ What volume of diluent is needed?

• From the first part, we need 25 mL insulin

– Insulin + diluent = total volume

– 25 + x = 225

– Subtracting 25 from both sides: x = 200

– 200 mL diluent is needed

© 2010 Delmar, Cengage Learning.

6

Concentrations

▪ Amount of a substance in a given volume

• Original concentration × dilution = final

concentration

• Find the final concentration if a saline solution

consisting of 10% NaCl is diluted using a 1/8

dilution

–.

© 2010 Delmar, Cengage Learning.

7

Concentrations (cont’d.)

▪ Find the final concentration:

• A saline solution consisting of 50% dextrose

is diluted using a 1/10 dilution

• .

© 2010 Delmar, Cengage Learning.

8

Concentrations and Volumes of

Two Solutions

▪ When a solution is diluted:

• Concentration of resulting solution will

decrease

• Formula used to find volumes and

concentrations of original and resulting

solutions:

© 2010 Delmar, Cengage Learning.

9

Concentrations and Volumes of

Two Solutions (cont’d.)

▪ There are 12cc of a 2.5% solution

• Solution added to water makes a total of

75cc

• What is the concentration of the 75 cc

solution?

–.

– 0.004 × 100% = .4%

© 2010 Delmar, Cengage Learning.

10

Concentrations and Volumes of

Two Solutions (cont’d.)

© 2010 Delmar, Cengage Learning.

11

Percents

▪ A percent weight per unit weight, % w/w, is

defined as:

• .

• Solute is the substance being dissolved

© 2010 Delmar, Cengage Learning.

12

Percents (cont’d.)

▪ Make 150 grams of a 20% w/w NaCl

solution

• .

x = 20g

100x = 3,000

x = 30

© 2010 Delmar, Cengage Learning.

13

Percents (cont’d.)

▪ A percent volume per unit volume, % v/v,

is defined as:

• .

• 5% v/v solution means that 5% of the entire

solution is the solute

© 2010 Delmar, Cengage Learning.

14

Percents (cont’d.)

▪ Make 50 mL of a 60% v/v solution of

hydrogen-peroxide in water

• .

•

x = 60

x = 30

• 30 mL hydrogen-peroxide added to 20 mL

water = 50-mL solution with a 60% v/v

© 2010 Delmar, Cengage Learning.

15

Percents (cont’d.)

▪ How many milliliters of alcohol are in 40mL

of a 60% v/v solution?

• .

100x = 2,400

•

x = 24

• There is 24mL alcohol in 40mL of a 60% v/v

solution

© 2010 Delmar, Cengage Learning.

16

Percents (cont’d.)

▪ A percent weight per unit volume, % w/v,

is defined as:

• That is, 5% w/v means that a 100-mL solution

would contain 5g solute

© 2010 Delmar, Cengage Learning.

17

Percents (cont’d.)

▪ How would you make 350mL of a 12% w/v

morphine solution?

• .

x = 12

100x = 4,200

x = 42

© 2010 Delmar, Cengage Learning.

18

Percents (cont’d.)

▪ How would you make 200mL of a 70% w/v

lidocaine solution?

• .

x = 70

100x = 14,000

x = 140

© 2010 Delmar, Cengage Learning.

19

Percents (cont’d.)

▪ How many grams of NaCl are in 25mL of a

0.9% w/v NaCl solution?

• A 0.9% w/v NaCl solution is called a normal

saline solution

• .

100x = 22.5

x = .225

© 2010 Delmar, Cengage Learning.

20

Percents (cont’d.)

▪ How many grams of NaOH (sodium

hydroxide) are in 6dL of a 20% w/v NaOH

solution?

• Convert dL to milliliters:

• .

100x = 12,000

x = 120

© 2010 Delmar, Cengage Learning.

21

Percents (cont’d.)

▪ A 500-cc solution contains 50g Tylenol

• What is the percentage of Tylenol?

• .

500x = 5,000

x = 10

© 2010 Delmar, Cengage Learning.

22

Summary

▪ Parts concentrate + parts diluent = total

volume

• Dilutions represent parts of concentrate in total

volume

• Original concentration × dilution = final

concentration

• Dilution factor is the reciprocal of dilution

© 2010 Delmar, Cengage Learning.

23

Summary (cont’d.)

▪ When a concentration and volume of a

solution change as a result of adding a

diluent:

• Used to find volume and concentration of

original and resulting solutions

▪ Percent weight per unit weight, % w/w:

© 2010 Delmar, Cengage Learning.

24

Summary (cont’d.)

▪ A percent weight per unit volume, % w/v:

▪ A percent volume per unit volume, % v/v:

© 2010 Delmar, Cengage Learning.

25

Part IB: DISCUSSION Chapter 3 (Measurement Systems and

Conversion Procedures), Chapter 4 (Dilutions, Solutions, and

Concentrations)

4040 unread replies.7070 replies.

Discussion Prompts: Discussion IB

(1) The key concept from Chapter 3 is dimensional analysis. What is your comfort level with

this idea of reducing the units in algebraic expressions to convert from one unit (or set of

units) to another?

(2) Chapter 4 builds on Chapter 3 and is of fundamental importance in this course. (Chapter

5 will continue to build on Chapter 4.) Share a specific tip with your colleagues in the class

on how you approach any of the types of problems in Chapter 4.

—————————-Please use this space to respond to the two discussion prompts I have provided above and for

any questions you have about course content from Chapters 3 and 4. If you have an answer

to a question that someone else has posted, please share your answer here. This is an

opportunity to help each other.

For help responding to a post, click here. (Links to an external site.)

Please remember course norms when posting to this discussion. Be polite and

respectful. Use full sentences and proper English spelling and grammar.

I will not generally post replies immediately in part because I want to give everyone a chance

to post answers to questions here.

NOTE: This is a graded discussion. You are expected to participate in the discussion of this

material. You should post to this discussion board at least 6 times (including your responses

to the discussion prompts).

———-I will count four things as “good” posts:

•

•

•

•

(1) Appropriate responses to the discussion prompts,

(2) (Nontrivial) Questions about the material that have not already been asked,

(3) Answers to questions that have not already been answered, and

(4) Posts that contribute to the sense of community and the sharing of

information. Note that (4) is a fairly broad category, and I will be fairly generous

when considering your posts, but the final decision for whether a post is deserving

of points is mine.

Please err on the side of too many posts rather than too few. These discussion boards are

here for you to help each other and to learn from each other.