Class Note: Converting Percentages to Fractions

Objective

Understand how to convert a percentage into a fraction.

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Step-by-Step Process

1. Convert Percentage to Decimal

   • Divide the percentage value by 100.
   • Example:
     • 30% → 30 ÷ 100 = 0.3
     • 15% → 15 ÷ 100 = 0.15
     • 12.8% → 12.8 ÷ 100 = 0.128

2. Convert Decimal to Fraction

   • Identify the decimal place (tenths, hundredths, thousandths, etc.).

   • Convert the decimal to a fraction accordingly:

     • Tenths: Multiply numerator and denominator by 10.
     • Hundredths: Multiply by 100.
     • Thousandths: Multiply by 1,000.

   • Example 1: 30%

     • Decimal: 0.3
     • Fraction: 0.3/1 × 10/10 = 3/10

   • Example 2: 15%

     • Decimal: 0.15
     • Fraction: 0.15/1 × 100/100 = 15/100
     • Simplify: 15 ÷ 5 = 3, 100 ÷ 5 = 20 → 15/100 = 3/20

   • Example 3: 12.8%

     • Decimal: 0.128
     • Fraction: 0.128/1 × 1,000/1,000 = 128/1,000
     • Simplifying:
       • 128 ÷ 2 = 64, 1,000 ÷ 2 = 500 → 64/500
       • 64 ÷ 2 = 32, 500 ÷ 2 = 250 → 32/250
       • 32 ÷ 2 = 16, 250 ÷ 2 = 125 → 16/125

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Summary Table

| Percentage | Decimal | Fraction | Simplified Fraction | |------------|---------|----------|--------------------| | 30% | 0.3 | 3/10 | 3/10 | | 15% | 0.15 | 15/100 | 3/20 | | 12.8% | 0.128 | 128/1000 | 16/125 |

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Key Points

• Always divide the percentage by 100 to get the decimal.
• Convert the decimal to a fraction by removing the decimal point (identify if it's tenths, hundredths, or thousandths).
• Always simplify the resulting fraction if possible.

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Formula Summary:

Percentage → (Divide by 100) → Decimal → (Convert to Fraction) → Simplify