What is Percentage?
Percentage is a way to express the relationship between a part and a whole, usually represented by the symbol "%". Percentage represents a number as a fraction of 100, for example, 50% represents 50/100, or one-half.
Percentage Calculation Formulas
- Calculate Percentage: \(\text{Percentage}= (\text{Value}\div \text{Total}) \times 100\%\)
- Calculate Value: \(\text{Value}= (\text{Percentage}\div 100) \times \text{Total}\)
- Calculate Total: \(\text{Total}= \text{Value}\div (\text{Percentage}\div 100)\)
Applications of Percentages
- Finance: Interest rates, discounts, growth rates, etc.
- Statistical Analysis: Data proportions, probability representation
- Education: Exam scores, grade assessment
- Business Decisions: Market share, profit margins, tax rates
Percentage Calculation Tips
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Converting Decimals to Percentages: Multiply by 100 and add the % symbol
- Example: 0.75 = 0.75 × 100% = 75%
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Converting Percentages to Decimals: Divide by 100 and remove the % symbol
- Example: 25% = 25 ÷ 100 = 0.25
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Percentage Increase/Decrease:
- Increase: [(New Value - Original Value) ÷ Original Value] × 100%
- Decrease: [(Original Value - New Value) ÷ Original Value] × 100%
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Compound Percentage Changes:
- Multiple percentage changes cannot be simply added
- Example: A 10% increase followed by another 10% increase is not a 20% increase, but a 21% increase (1.1 × 1.1 = 1.21)