Lecture on Converting Between Percents, Decimals, and Fractions

Introduction

• Topic: Converting between percents, decimals, and fractions.
• Methods: Percent to decimal, decimal to percent, decimal to fraction, fraction to decimal, percent to fraction, and fraction to percent.

Decimal to Percent

• Method: Multiply the decimal by 100 or move the decimal two places to the right.
• Example: Convert 0.23 to a percent:
  • Multiply by 100: 0.23 * 100 = 23%
  • Move decimal two places: 0.23 becomes 23%*

Percent to Decimal

• Method: Divide the percent by 100 or move the decimal two places to the left.
• Example: Convert 15% to a decimal:
  • Divide by 100: 15 / 100 = 0.15
  • Move decimal two places: 15% becomes 0.15

Tricky Examples

• For large percents or small decimals, use multiplying/dividing by 100 to avoid confusion.
  • Example: Convert 245% to decimal: 245 / 100 = 2.45
  • Example: Convert 0.036 to percent: 0.036 * 100 = 3.6%*

Decimal to Fraction

• Concept: Recognize place values (tenths, hundredths, thousandths).
• Method: Write the decimal as a fraction using place values.
• Example: 0.111 is 111/1000 (thousandths place)

Fraction to Decimal

• Method: Division of the numerator by the denominator.
• Example: Convert 7/8 to decimal:
  • Long division: 7 divided by 8 = 0.875

Percent to Fraction

• Method: Convert percent to decimal, then decimal to fraction, or directly put the percent over 100.
• Example: Convert 80% to a fraction:
  • 80% is 80/100 = 4/5 (simplified)

Fraction to Percent

• Method: Convert fraction to decimal, then decimal to percent.
• Example: Convert 1/4 to a percent:
  • 1/4 = 0.25, then 0.25 * 100 = 25%*

Summary

• Conversion methods: Percent to decimal, decimal to fraction, and percent to fraction.
• Emphasis on understanding how each conversion builds upon the others.
• Encouragement to practice these conversions regularly.

Final Note

• Using calculators is recommended for checking work, especially with complex decimals.
• Understanding the process helps in reducing errors during conversion.