2. Pie Charts and Percentages

Pie charts divide a whole into slices, where each slice represents a part of the total. The whole circle always represents 100%.

Reading a pie chart:

1. Identify the title and what each slice represents.
2. Read the percentages (or angles) for each slice.
3. Interpret the relative sizes: a larger slice means a larger percentage.
4. Add percentages to verify: they should sum to 100%.

Converting pie chart percentages to angles:
Since a full circle has 360°, multiply the percentage by 360° to find the angle.

Example: If a slice represents 25% of the budget:
\[ \text{Angle} = 0.25 \times 360° = 90° \]

Finding amounts from percentages:
If a pie chart shows 40% of a $2,000 budget spent on rent:
\[ \text{Rent} = 0.40 \times 2,000 = 800 \text{ dollars} \]

Real-world context: A company pie chart shows that 35% of employees work in sales, 25% in operations, and 40% in support. If there are 200 employees total:

• Sales: \(0.35 \times 200 = 70\) employees
• Operations: \(0.25 \times 200 = 50\) employees
• Support: \(0.40 \times 200 = 80\) employees

Common mistake: forgetting that percentages must sum to 100%. If a chart shows 30%, 40%, and 25%, something is missing (5%).

💡 Tip: Draw a mental line from the center to see angles. A quarter of a circle is 90° (25%), a half is 180° (50%), and a three-quarter is 270° (75%).