### **What is a Percentage?** A **percentage** is a way of expressing a number as a fraction of 100. It helps compare values, analyze data, and measure proportions. The symbol "%" represents a percentage. For example, if a school has **200 students**, and **50** of them are in the music club, the percentage of students in the club is calculated as: \[ (50 ÷ 200) × 100 = 25\% \] This means **25% of the students** participate in the music club. ### **How to Calculate a Percentage** To determine a percentage, use the formula: \[ \left( \frac{\text{Part}}{\text{Whole}} \right) × 100 \] Where: - **Part** = the specific portion you are measuring - **Whole** = the total amount For instance, if a fruit basket contains **120 fruits**, and **36 of them are oranges**, the percentage of oranges in the basket is: \[ (36 ÷ 120) × 100 = 30\% \] So, **30% of the fruits** are oranges. ### **How to Convert Percentages** Percentages can be converted into fractions or decimals: - **To convert a percentage to a decimal**, divide by 100. - Example: **75% = 75 ÷ 100 = 0.75** - **To convert a decimal to a percentage**, multiply by 100. - Example: **0.6 × 100 = 60%** - **To convert a percentage to a fraction**, place it over 100 and simplify. - Example: **40% = 40/100 = 2/5** ### **Why Percentages Matter** Percentages are widely used in everyday life, including: - **Finance & Shopping:** - A **20% discount** on a **$50** item saves you **$10** (since \(50 × 0.2 = 10\)). - A bank offering **5% interest** on a **$1,000** savings account earns you **$50** per year. - **Data Analysis & Statistics:** - A survey finding that **60% of people prefer coffee** over tea shows a preference trend. - Election results often show the percentage of votes each candidate received. - **Business & Economics:** - A company’s sales increase from **$10,000 to $12,000** means a **20% growth**: \[ \left( \frac{12,000 - 10,000}{10,000} \right) × 100 = 20\% \] - **Health & Fitness:** - If **25% of a daily 2,000-calorie diet** comes from protein, that equals **500 calories from protein**. Understanding percentages is essential for making informed decisions, interpreting data, and managing finances effectively.