Notes on Converting Fractions to Decimals

Introduction

• Presenter: Mr. J
• Topic: Converting fractions to decimals
• Key Instruction: Divide the numerator by the denominator and round if necessary.

Process Overview

• Long division is used to convert fractions to decimals.
• Use a calculator for quicker conversions and interpretation of results.

Examples:

Example 1: 2/5

• Calculation: 2 divided by 5
• Since 2 < 5, add a decimal and a zero: 20
• Division:
  • How many 5s in 20? Answer: 4
  • 4 x 5 = 20
  • Remainder = 0
• Result: 2/5 = 0.4 (or 4 tenths)

Example 2: 9/25

• Calculation: 9 divided by 25
• Since 9 < 25, add a decimal and a zero: 90
• Division:
  • How many 25s in 90? Answer: 3
  • 3 x 25 = 75
  • Remainder = 15
• Add another zero: 150
• How many 25s in 150? Answer: 6
  • 6 x 25 = 150
  • Remainder = 0
• Result: 9/25 = 0.36 (or 36 hundredths)

Example 3: 3/16

• Calculation: 3 divided by 16
• Use a calculator for this, result is 0.1875
• Rounding: Round to the thousandths (0.188) because we look at the digit next door (5) which rounds up.
• Result: 3/16 = 0.188 (rounded)

Example 4: 1/3

• Calculation: 1 divided by 3
• Add decimal and zero: 10
• Division:
  • How many 3s in 10? Answer: 3
  • Remainder = 1
• Repeat adding zeros: always get 10, so it’s a repeating decimal
• Result: 1/3 = 0.333... (or rounded to 0.333)
• Notation: Use a bar over the 3 to denote it repeats.

Example 5: 17/11

• Calculation: 17 divided by 11
• Result from calculator: 1.545454...
• Rounding: Round to the thousandths (1.545) because the next digit (4) stays the same.
• Result: 17/11 = 1.545 (rounded) or 1.54 with a bar over 54.

Example 6: 17/20

• Calculation: 17 divided by 20
• Result: 0.85 (exact, no rounding needed)

Conclusion

• Summary of Key Points:
  • Divide numerator by denominator.
  • Interpret the result:
    • Round if necessary.
    • Identify if it's a repeating decimal or terminates in a specific place.
• Thank you for watching!