Comprehensive Guide for Nursing Students and Healthcare
TABLE OF CONTENTS
1. Basic Mathematical Foundations
2. Unit Conversions and Dimensional Analysis
3. Ratio and Proportion Method
4. Formula Method
5. Oral Medications
6. Injectable Medications
7. IV Flow Rate Calculations
8. Pediatric and Geriatric Dosages
9. Critical Care and High-Alert Medications
10. Practice Problems with Answer Keys
CHAPTER 1: BASIC MATHEMATICAL FOUNDATIONS
Learning Objectives
By the end of this chapter, you will be able to:
• Convert between fractions, decimals, and percentages
, • Perform basic arithmetic operations accurately
• Round numbers appropriately for medication calculations
• Apply mathematical principles to dosage calculations
1.1 Fractions, Decimals, and Percentages
Converting Fractions to Decimals:
• Divide the numerator by the denominator
• Example: 3/4 = 3 ÷ 4 = 0.75
Converting Decimals to Percentages:
• Multiply by 100 and add % sign
• Example: 0.75 × 100 = 75%
Practice Problem 1.1: Convert the following: a) 2/5 to decimal:
___________ b) 0.25 to percentage: ___________ c) 60% to
decimal: ___________
Answers: a) 0.4 b) 25% c) 0.6
1.2 Rounding Rules for Medications
General Rounding Rules:
• Whole numbers: Round to nearest whole number
• Dosages < 1 mL: Round to nearest hundredth (0.01)
• Dosages ≥ 1 mL: Round to nearest tenth (0.1)
• Never round until the final calculation
, Example 1.2: Calculate: 2.347 mL for injection Step 1: Identify
rounding requirement (≥ 1 mL = nearest tenth) Step 2: Look at
hundredths place (4) Step 3: Since 4 < 5, round down to 2.3 mL
CHAPTER 2: UNIT CONVERSIONS AND DIMENSIONAL ANALYSIS
2.1 Metric System Conversions
Common Conversions:
• 1 kg = 1000 g
• 1 g = 1000 mg
• 1 mg = 1000 mcg
• 1 L = 1000 mL
Dimensional Analysis Method: Use conversion factors to cancel
unwanted units
Example 2.1: Convert 2.5 kg to grams
Step-by-Step Solution:
2.5 kg × (1000 g/1 kg) = 2500 g
Setup: Start with given → multiply by conversion factor →
unwanted units cancel
Practice Problem 2.1: Convert 750 mg to grams Answer: 0.75 g
2.2 Household to Metric Conversions
TABLE OF CONTENTS
1. Basic Mathematical Foundations
2. Unit Conversions and Dimensional Analysis
3. Ratio and Proportion Method
4. Formula Method
5. Oral Medications
6. Injectable Medications
7. IV Flow Rate Calculations
8. Pediatric and Geriatric Dosages
9. Critical Care and High-Alert Medications
10. Practice Problems with Answer Keys
CHAPTER 1: BASIC MATHEMATICAL FOUNDATIONS
Learning Objectives
By the end of this chapter, you will be able to:
• Convert between fractions, decimals, and percentages
, • Perform basic arithmetic operations accurately
• Round numbers appropriately for medication calculations
• Apply mathematical principles to dosage calculations
1.1 Fractions, Decimals, and Percentages
Converting Fractions to Decimals:
• Divide the numerator by the denominator
• Example: 3/4 = 3 ÷ 4 = 0.75
Converting Decimals to Percentages:
• Multiply by 100 and add % sign
• Example: 0.75 × 100 = 75%
Practice Problem 1.1: Convert the following: a) 2/5 to decimal:
___________ b) 0.25 to percentage: ___________ c) 60% to
decimal: ___________
Answers: a) 0.4 b) 25% c) 0.6
1.2 Rounding Rules for Medications
General Rounding Rules:
• Whole numbers: Round to nearest whole number
• Dosages < 1 mL: Round to nearest hundredth (0.01)
• Dosages ≥ 1 mL: Round to nearest tenth (0.1)
• Never round until the final calculation
, Example 1.2: Calculate: 2.347 mL for injection Step 1: Identify
rounding requirement (≥ 1 mL = nearest tenth) Step 2: Look at
hundredths place (4) Step 3: Since 4 < 5, round down to 2.3 mL
CHAPTER 2: UNIT CONVERSIONS AND DIMENSIONAL ANALYSIS
2.1 Metric System Conversions
Common Conversions:
• 1 kg = 1000 g
• 1 g = 1000 mg
• 1 mg = 1000 mcg
• 1 L = 1000 mL
Dimensional Analysis Method: Use conversion factors to cancel
unwanted units
Example 2.1: Convert 2.5 kg to grams
Step-by-Step Solution:
2.5 kg × (1000 g/1 kg) = 2500 g
Setup: Start with given → multiply by conversion factor →
unwanted units cancel
Practice Problem 2.1: Convert 750 mg to grams Answer: 0.75 g
2.2 Household to Metric Conversions
