Math Antics: Introduction to Percentages

Importance of Percentages

• Percentages are frequently used in real-life scenarios:
  • Calculating sales tax
  • Determining sale prices
  • Measuring nutritional content (e.g., fiber in granola bars)
  • Calculating investment returns

Understanding Percentages

• Key Concept: A percent is a fraction with 100 as the denominator.
• Percent Sign (%): Indicates that a number is a percentage.

Definition and Meaning

• The term "percent" literally means "per 100".
• A percentage like 15% is equivalent to the fraction 15/100.

Examples of Percentages as Fractions

• 3% = 3/100
• 10% = 10/100
• 25% = 25/100
• 75% = 75/100

Special Cases in Percentages

• 0%: Equivalent to 0/100, known as a "zero fraction" (value = 0).
• 100%: Equivalent to 100/100, known as a "whole fraction" (value = 1).
• >100%: For example, 126% = 126/100, an "improper fraction" (value > 1).

Converting Percentages to Decimals

• Percentages are base-10 fractions with 100 as the denominator.
• Conversion Trick:
  1. Identify the decimal point in the number (e.g., 35 would be 35.0).
  2. Move the decimal point two places to the left.
  3. Remove the percent sign.

Examples

• 15% becomes 0.15
• 62% becomes 0.62
• 75% becomes 0.75
• 99% becomes 0.99
• 4% becomes 0.04 (using a zero as a placeholder)
• 1% becomes 0.01
• 0% is 0.00
• 100% becomes 1.00
• 142% becomes 1.42

Converting Fractions and Decimals to Percentages

• Fractions with 100 as the denominator can be converted to percentages.
  • 12/100 is 12%
  • 80/100 is 80%
• Decimals can also be converted:
  • 0.10 is 10%
  • 0.38 is 38%

Conclusion

• Percentages are another way to express fractions and decimals.
• Understanding basics of percentages is crucial, and further applications will be discussed in future resources.

Learn more at www.mathantics.com