Key Takeaways
- To convert decimal to percentage, multiply by 100; percentage to decimal, divide by 100
- Memorize common fraction-decimal-percentage equivalents (1/4 = 0.25 = 25%)
- Percent of a number: convert to decimal and multiply
- Percent change: (New - Original) / Original × 100
- When multiplying decimals, count total decimal places for the answer
Decimals and Percentages
Decimals and percentages are used constantly in healthcare for dosage calculations, vital signs, and lab values. Understanding conversions between fractions, decimals, and percentages is essential.
Decimal Place Values
| Place | Value | Example (in 0.375) |
|---|---|---|
| Tenths | 0.1 | 3 (represents 0.3) |
| Hundredths | 0.01 | 7 (represents 0.07) |
| Thousandths | 0.001 | 5 (represents 0.005) |
Decimal Operations
Adding/Subtracting Decimals:
- Line up decimal points
- Add zeros as placeholders if needed
- Add or subtract normally
- Place decimal point in answer
Example: 3.45 + 2.6
3.45
+ 2.60
------
6.05
Multiplying Decimals:
- Multiply as if no decimals
- Count total decimal places in both numbers
- Place decimal in answer with that many places
Example: 1.5 × 2.4
- 15 × 24 = 360
- Total decimal places: 2
- Answer: 3.60 = 3.6
Dividing Decimals:
- Move decimal in divisor to make it a whole number
- Move decimal in dividend the same number of places
- Divide normally
- Place decimal directly above in quotient
Example: 4.5 ÷ 0.5
- Move decimal: 45 ÷ 5
- Answer: 9
Converting Between Fractions, Decimals, and Percentages
| From | To | Method | Example |
|---|---|---|---|
| Fraction → Decimal | Divide | ¾ → 3 ÷ 4 = 0.75 | |
| Decimal → Fraction | Place value | 0.75 = 75/100 = 3/4 | |
| Decimal → Percentage | × 100 | 0.75 × 100 = 75% | |
| Percentage → Decimal | ÷ 100 | 75% ÷ 100 = 0.75 | |
| Fraction → Percentage | ÷ then × 100 | ¾ = 0.75 = 75% | |
| Percentage → Fraction | ÷ 100, simplify | 75% = 75/100 = 3/4 |
Common Conversions to Memorize
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333... | 33.3% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.666... | 66.7% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
Percentage Calculations
Finding a Percentage of a Number: Convert percentage to decimal and multiply.
Example: What is 15% of 80?
- 15% = 0.15
- 0.15 × 80 = 12
Finding What Percent One Number Is of Another: Divide the part by the whole, then multiply by 100.
Example: 15 is what percent of 60?
- 15 ÷ 60 = 0.25
- 0.25 × 100 = 25%
Finding the Whole When Given a Percentage: Divide the part by the percentage (as decimal).
Example: 12 is 20% of what number?
- 12 ÷ 0.20 = 60
Percent Change
Percent Change = (New - Original) / Original × 100
Example: Weight dropped from 200 lbs to 180 lbs. What is the percent decrease?
- Change: 180 - 200 = -20
- Percent: (-20 ÷ 200) × 100 = -10%
- Answer: 10% decrease
Rounding Decimals
Steps to Round:
- Identify the place to round to
- Look at the digit to the right
- If 5 or greater, round up; if less than 5, round down
Example: Round 3.7846 to the nearest hundredth
- Hundredths digit: 8
- Digit to the right: 4 (less than 5)
- Answer: 3.78
Healthcare Applications
| Application | Example |
|---|---|
| Medication concentration | 0.5 mg/mL |
| Lab values | Blood glucose: 95.5 mg/dL |
| IV rates | 125.5 mL/hour |
| Dosage calculation | 25% solution |
| Body composition | 18.5% body fat |
Convert 0.625 to a fraction in simplest form.
What is 35% of 240?
A patient's weight changed from 180 lbs to 171 lbs. What is the percent change?