Overview
This lecture explains how to convert between fractions, decimals, and percentages, including step-by-step methods and examples for each conversion.
Introduction to Number Forms
- Fractions, decimals, and percentages all represent parts of a whole.
- Understanding how to convert between these forms is essential for math problems.
Converting Decimals and Percentages
- To convert a decimal to a percentage, multiply by 100 (e.g., 0.3 × 100 = 30%).
- To convert a percentage to a decimal, divide by 100 (e.g., 30% ÷ 100 = 0.3).
Converting Percentages and Fractions
- To change a percentage to a fraction, write it over 100 and simplify (e.g., 35% = 35/100 = 7/20).
- To convert a fraction to a percentage, make the denominator 100 or multiply by 100 (e.g., 3/10 × 10/10 = 30/100 = 30%).
Converting Fractions and Decimals
- To convert a fraction to a decimal, divide the numerator by the denominator (e.g., 7/10 = 0.7).
- If the denominator doesn’t divide easily into 100 or 10, use division (e.g., 1/6 = 0.166... recurring).
- Calculators can convert between all forms using the appropriate buttons.
Worked Examples and Practice
- Practice converting decimals to percentages: 0.88 → 88%, 0.01 → 1%, 0.3 → 30%, etc.
- Practice converting percentages to decimals: 34% → 0.34, 12% → 0.12, etc.
- Practice converting percentages to fractions: 2% → 1/50, 15% → 3/20.
- Practice converting fractions to percentages: 3/10 = 30%, 11/20 = 55%, 6/25 = 24%.
- Practice converting fractions to decimals: 21/50 = 0.42, 3/5 = 0.6, 2/3 = 0.66... recurring.
Summary Table Examples
- 1/4 = 0.25 = 25%
- 0.2 = 20% = 1/5
- 36% = 0.36 = 9/25
- 0.18 = 18% = 9/50
- 1/3 = 0.333... = 33.3...%
- 4% = 0.04 = 1/25
Key Terms & Definitions
- Decimal — A number with a point representing part of a whole (e.g., 0.25).
- Percentage (%) — A number out of 100 (e.g., 25% equals 25 out of 100).
- Fraction — A number showing part of a whole with numerator and denominator (e.g., 1/4).
- Recurring Decimal — A decimal with repeating digits (e.g., 0.333...).
Action Items / Next Steps
- Practice converting between all three forms using example problems.
- Complete the summary table for fractions, decimals, and percentages not covered in class.
- Use a calculator for more complex conversions as needed.