percentage LEC. 4

Percentages are a way of expressing a number as a fraction of 100. They are commonly used to compare quantities, represent proportions, and describe changes over time. Here are some key points about percentages:
1. **Definition**: A percentage is a fraction where the denominator is always 100. For example, 25% is equivalent to \( \frac{25}{100} \), which simplifies to \( 0.25 \) or 25 out of 100.
2. **Symbol**: The percentage symbol is "%". For instance, 50% means 50 out of 100, or half.
3. **Calculations**: Percentages can be calculated by multiplying the decimal form of the percentage by the whole quantity. For example, finding 20% of 80 involves calculating \( 0.2 \times 80 = 16 \).
4. **Applications**: Percentages are used in various real-world scenarios such as:
- Calculating discounts (e.g., 20% off).
- Expressing interest rates (e.g., 5% annual interest).
- Describing proportions and distributions (e.g., 70% of the population).
5. **Percentage Points vs. Percent**: "Percentage points" are the difference between two percentages (e.g., an increase from 10% to 15% is a 5 percentage point increase). "Percent" refers to the actual proportion out of 100 (e.g., a 5% increase).
Understanding percentages is essential for interpreting data, making financial decisions, and analyzing trends in various fields like economics, statistics, and everyday life.

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