Converting Decimals to Fractions

General Process

1. Identify the number of digits to the right of the decimal.
2. Place the decimal number over 1 (write it as a fraction).
3. Multiply both the numerator and the denominator by 10 raised to the power of the number of decimal places.
4. Simplify the resulting fraction.

Examples

Example 1: Convert 0.3 to a fraction

• Step 1: One digit to the right of the decimal (tenths place)
• Step 2: Write 0.3 as a fraction: 0.3/1
• Step 3: Multiply numerator and denominator by 10
  • 0.3 * 10 = 3
  • 1 * 10 = 10
• Result: 3/10

Example 2: Convert 0.36 to a fraction

• Step 1: Two digits to the right of the decimal (hundredths place)
• Step 2: Write 0.36 as a fraction: 0.36/1
• Step 3: Multiply numerator and denominator by 100
  • 0.36 * 100 = 36
  • 1 * 100 = 100
• Step 4: Simplify
  • Both 36 and 100 are divisible by 4
  • 36 / 4 = 9
  • 100 / 4 = 25
• Result: 9/25

Example 3: Convert 3.75 to a fraction

• Step 1: Two digits to the right of the decimal (hundredths place)
• Step 2: Write 3.75 as a fraction: 3.75/1
• Step 3: Multiply numerator and denominator by 100
  • 3.75 * 100 = 375
  • 1 * 100 = 100
• Step 4: Simplify
  • Both 375 and 100 are divisible by 5
  • 375 / 5 = 75
  • 100 / 5 = 20
  • 75 and 20 are also divisible by 5
  • 75 / 5 = 15
  • 20 / 5 = 4
• Result: 15/4 (this is equal to 3.75)

Example 4: Convert 0.284 to a fraction

• Step 1: Three digits to the right of the decimal (thousandths place)
• Step 2: Write 0.284 as a fraction: 0.284/1
• Step 3: Multiply numerator and denominator by 1000
  • 0.284 * 1000 = 284
  • 1 * 1000 = 1000
• Step 4: Simplify
  • Both 284 and 1000 are divisible by 2 (they are even numbers)
  • 284 / 2 = 142
  • 1000 / 2 = 500
  • 142 and 500 are also divisible by 2
  • 142 / 2 = 71
  • 500 / 2 = 250
  • 71 and 250 cannot be simplified further
• Result: 71/250

Key Points

• The number of decimal places determines the power of 10 by which to multiply.
• Always simplify the fraction at the end.
• Use common divisors to reduce the fraction.