DIMENSION ANALYSIS –
CALCULATING DOSAGES
ND
SAFELY 2 EDITION
SUMMARY GUIDE
, Brief Contents
Arithmetic Skills Assessment
UNIT 1: Arithmetic Review and Dimensional Analysis 1
Chapter 1 Whole Numbers 1
Chapter 2 Fractions 15
Chapter 3 Decimals and Percents 34
Chapter 4 Dimensional Analysis 55
Unit I Post-Test 69
UNIT 2: Medication Administration 71
Chapter 5 Measures and Equivalents 71
Chapter 6 Conversions 79
Chapter 7 Safety Considerations in Medication Administration 92
Chapter 8 Prescriptio ns and Medication Orders 116
Chapter 9 Reading Medication Labels and Syringes 132
Chapter 10 Reconstituting Parenteral Medications From a Powder 168
Chapter 11 Calculations Using Weight and Body Surface Area 179
Chapter 12 Intravenous Delivery Systems and Equipment 201
Chapter 13 Intravenous Calculations 218
Unit II Post-Test 257
Chapter 14 Enteral Tube Feedings 265
Chapter 15 Insulin Administration 293
Chapter 16 Heparin Administration 319
Chapter 17 Critical Care Dosage Calculations 345
Chapter 18 Lifespan Considerations in Dosage Calculation 371
Unit III Post-Test 397
Comprehe nsiv e Post-Te st 405
UNIT 4: Test Answers 413
Appendices
Appendix A: Calculators 435
Appendix B: Roman Numerals 437
Appendix C: The 24-Hour Clock 439
, UNIT 1
Arithmetic Review
and Dimensional
Analysis
Chapter 1
Whole Numbers
Glossary
Dividend: The number that is to be divided into parts.
Difference: The amount that remains after one number is subtracted from
another.
Divisor: The number by which the dividend is to be divided.
Equation: A mathematical statement (for example: 5 + 3 = 8).
Product: The answer reached when two numbers are multiplied.
Quotient: The answer reached when dividing one number (the dividend)
by another number (the divisor).
Sum: The amount obtained after adding one number to another.
Whole number: A number that does not contain fractions, decimals, or
negative numbers.
1
,
,2 UNIT I Arithmetic Review and Dimensional Analysis
Objectives
After completing this chapter, the learner will be able to—
1. Define whole number.
2. Add whole numbers.
3. Subtract whole numbers.
4. Multiply whole numbers.
5. Divide whole numbers.
Types of Numbers
Nu mbers ca n be clas sifie d in sev eral differe nt w ay s. They ca n be ex pres sed a s inte gers, ratio na l
nu mber s, irr ational nu m bers, re al nu mber s, prime n u mbers, factors, whole n u mbers, fr actions, or
decim als (see Box 1 -1 ). Ad ding, s ubtractin g, m ultiply in g, an d div id in g n u mbers mu st be com plete d
in a certa in or der (se e Box 1 -2 a nd Box 1 -3 ). This cha pter rev iew s ad ding, s ubtractin g, m ultiply in g,
and div iding whole numbers.
■ Box 1-1 Types of Numbers
Integers
Integers are positive and negative whole numbers.
Examples: 3, 2, 1, 0, —1, —2, —3, . . .
Rational Numbers
Rational numbers include integers and fractions.
1 4
Examples: —1, —0.5, — , , 0.7, 1, 2, . . .
2 5
Irrational Numbers
Irrational numbers are those that have nonrepeating decimal places.
Example: π = 3.14159 . . .
Real Numbers
Real numbers encompass both rational and irrational numbers.
Prime Numbers
A prime number can be evenly divided by only 1 and itself.
Examples: 1, 3, 5, 7, 11, . . .
Factors
Factors are numbers that divide evenly into another number.
Example : The factors of 20 are 1, 2, 4, 5, and 10.
Whole Numbers
Whole numbers do not contain fractions, decimals, or negative numbers.
Examples : 4, 8, 25, 102, 1429, . . .
Fractions
Fractions are numbers that are part of a whole number.
2 4 3 9
Examples : , , , , . . .
3 5 10 17
Decimals
Decimals are numbers that represent a part of a whole number, and/or may be a combination of a whole number
and a part of a number.
Examples: 0.25, 3.1, 10.164, 184.3, . . .
, Chapter 1 Whole Numbers 3
■ Box 1-2 Properties of Numbers
Commutative Property of Numbers
This property applies to operations of addition and multiplication only. The order of operations can be changed
without affecting the final answer.
a +b= b+ a
a ×b =b ×a
Example: 2 + 3 = 5
3+2=5
Example: 2 × 3 = 6
3×2=6
Associative Property of Numbers
This property also applies to operations of addition and multiplication only. Operations may be grouped differently
without affecting the final answer.
(a + b) + c = a + (b + c)
(a × b) × c = a × (b × c)
Example: (2 + 3) + 4 = 9
2 + (3 + 4) = 9
Example: (2 × 3) × 4 = 24
2 × (3 × 4) = 24
Distributive Property of Numbers
This property shows how equations with multiplication and addition operations can be broken into smaller pieces.
a × (b + c) = (a × b) + (a × c)
Example: 10 × (2 + 3) = 50
(10 × 2) + (10 × 3) = 50
■ Box 1-3 Order of Mathematical Operations
1. Perform operations that are inside the parentheses first.
2. Perform the operations that require multiplying or dividing first, starting from left to right.
3. Perform the operations that require adding or subtracting next, starting from left to right.
Whole Numbers
Whol e numbers are also called nat ural nu m bers or cou nting nu mber s. They include the nu mb er 0
and a ll posit iv e num bers, suc h a s 1, 2, 3 , 4 , a nd so on. Add in g, subtr actin g, an d m ultiply in g whole
nu mber s re sult in a ns wer s t hat are w hole nu m bers. Div iding w hole n u mbers may resu lt in a frac -
tion or decimal. Figure 1 -1 shows the place v alues of numbers up to the sev enth (or millions) place.
Hundred thousands
Ten thousands
Thousands
Hundreds
Millions
Ones
Tens
Figure 1-1 Place Value of Whole Numbers. These are the place values for the whole
1, 3 4 3, 7 2 9 num ber 1 ,343,729.
CALCULATING DOSAGES
ND
SAFELY 2 EDITION
SUMMARY GUIDE
, Brief Contents
Arithmetic Skills Assessment
UNIT 1: Arithmetic Review and Dimensional Analysis 1
Chapter 1 Whole Numbers 1
Chapter 2 Fractions 15
Chapter 3 Decimals and Percents 34
Chapter 4 Dimensional Analysis 55
Unit I Post-Test 69
UNIT 2: Medication Administration 71
Chapter 5 Measures and Equivalents 71
Chapter 6 Conversions 79
Chapter 7 Safety Considerations in Medication Administration 92
Chapter 8 Prescriptio ns and Medication Orders 116
Chapter 9 Reading Medication Labels and Syringes 132
Chapter 10 Reconstituting Parenteral Medications From a Powder 168
Chapter 11 Calculations Using Weight and Body Surface Area 179
Chapter 12 Intravenous Delivery Systems and Equipment 201
Chapter 13 Intravenous Calculations 218
Unit II Post-Test 257
Chapter 14 Enteral Tube Feedings 265
Chapter 15 Insulin Administration 293
Chapter 16 Heparin Administration 319
Chapter 17 Critical Care Dosage Calculations 345
Chapter 18 Lifespan Considerations in Dosage Calculation 371
Unit III Post-Test 397
Comprehe nsiv e Post-Te st 405
UNIT 4: Test Answers 413
Appendices
Appendix A: Calculators 435
Appendix B: Roman Numerals 437
Appendix C: The 24-Hour Clock 439
, UNIT 1
Arithmetic Review
and Dimensional
Analysis
Chapter 1
Whole Numbers
Glossary
Dividend: The number that is to be divided into parts.
Difference: The amount that remains after one number is subtracted from
another.
Divisor: The number by which the dividend is to be divided.
Equation: A mathematical statement (for example: 5 + 3 = 8).
Product: The answer reached when two numbers are multiplied.
Quotient: The answer reached when dividing one number (the dividend)
by another number (the divisor).
Sum: The amount obtained after adding one number to another.
Whole number: A number that does not contain fractions, decimals, or
negative numbers.
1
,
,2 UNIT I Arithmetic Review and Dimensional Analysis
Objectives
After completing this chapter, the learner will be able to—
1. Define whole number.
2. Add whole numbers.
3. Subtract whole numbers.
4. Multiply whole numbers.
5. Divide whole numbers.
Types of Numbers
Nu mbers ca n be clas sifie d in sev eral differe nt w ay s. They ca n be ex pres sed a s inte gers, ratio na l
nu mber s, irr ational nu m bers, re al nu mber s, prime n u mbers, factors, whole n u mbers, fr actions, or
decim als (see Box 1 -1 ). Ad ding, s ubtractin g, m ultiply in g, an d div id in g n u mbers mu st be com plete d
in a certa in or der (se e Box 1 -2 a nd Box 1 -3 ). This cha pter rev iew s ad ding, s ubtractin g, m ultiply in g,
and div iding whole numbers.
■ Box 1-1 Types of Numbers
Integers
Integers are positive and negative whole numbers.
Examples: 3, 2, 1, 0, —1, —2, —3, . . .
Rational Numbers
Rational numbers include integers and fractions.
1 4
Examples: —1, —0.5, — , , 0.7, 1, 2, . . .
2 5
Irrational Numbers
Irrational numbers are those that have nonrepeating decimal places.
Example: π = 3.14159 . . .
Real Numbers
Real numbers encompass both rational and irrational numbers.
Prime Numbers
A prime number can be evenly divided by only 1 and itself.
Examples: 1, 3, 5, 7, 11, . . .
Factors
Factors are numbers that divide evenly into another number.
Example : The factors of 20 are 1, 2, 4, 5, and 10.
Whole Numbers
Whole numbers do not contain fractions, decimals, or negative numbers.
Examples : 4, 8, 25, 102, 1429, . . .
Fractions
Fractions are numbers that are part of a whole number.
2 4 3 9
Examples : , , , , . . .
3 5 10 17
Decimals
Decimals are numbers that represent a part of a whole number, and/or may be a combination of a whole number
and a part of a number.
Examples: 0.25, 3.1, 10.164, 184.3, . . .
, Chapter 1 Whole Numbers 3
■ Box 1-2 Properties of Numbers
Commutative Property of Numbers
This property applies to operations of addition and multiplication only. The order of operations can be changed
without affecting the final answer.
a +b= b+ a
a ×b =b ×a
Example: 2 + 3 = 5
3+2=5
Example: 2 × 3 = 6
3×2=6
Associative Property of Numbers
This property also applies to operations of addition and multiplication only. Operations may be grouped differently
without affecting the final answer.
(a + b) + c = a + (b + c)
(a × b) × c = a × (b × c)
Example: (2 + 3) + 4 = 9
2 + (3 + 4) = 9
Example: (2 × 3) × 4 = 24
2 × (3 × 4) = 24
Distributive Property of Numbers
This property shows how equations with multiplication and addition operations can be broken into smaller pieces.
a × (b + c) = (a × b) + (a × c)
Example: 10 × (2 + 3) = 50
(10 × 2) + (10 × 3) = 50
■ Box 1-3 Order of Mathematical Operations
1. Perform operations that are inside the parentheses first.
2. Perform the operations that require multiplying or dividing first, starting from left to right.
3. Perform the operations that require adding or subtracting next, starting from left to right.
Whole Numbers
Whol e numbers are also called nat ural nu m bers or cou nting nu mber s. They include the nu mb er 0
and a ll posit iv e num bers, suc h a s 1, 2, 3 , 4 , a nd so on. Add in g, subtr actin g, an d m ultiply in g whole
nu mber s re sult in a ns wer s t hat are w hole nu m bers. Div iding w hole n u mbers may resu lt in a frac -
tion or decimal. Figure 1 -1 shows the place v alues of numbers up to the sev enth (or millions) place.
Hundred thousands
Ten thousands
Thousands
Hundreds
Millions
Ones
Tens
Figure 1-1 Place Value of Whole Numbers. These are the place values for the whole
1, 3 4 3, 7 2 9 num ber 1 ,343,729.
