Ordering Numbers and Percentages

Ordering Numbers and Percentages

Key Concepts

  • Understanding Number Comparison
    • The task is to order numbers and percentages from smallest to largest.

Values to Compare

  • The given values are:
    • 0.6
    • 70%
    • 0.75
    • 2/3

Definitions and Conversions

  • Decimal and Percentage:
    • 0.6 is the decimal form of 60%.
    • 70% can be converted into decimal form as follows:
    • 70 ext{%} = 0.70
    • 0.75 is already in decimal form.
    • 2/3 (fraction) needs to be converted into decimal:
    • rac23ext(asadecimal)≈0.6667rac{2}{3} ext{ (as a decimal)} \approx 0.6667

Arranging the Values

  • Converting all values into decimal forms:

    • 0.6 = 0.6
    • 70% = 0.70
    • 0.75 = 0.75
    • 2/3 ≈ 0.6667

  • Now, we can order the values:

    • Comparing:
    • 0.6 < 0.6667 < 0.70 < 0.75

Final Ordering

  • The correct order from smallest to largest is:
    • 0.6 < rac{2}{3} < 70 ext{%} < 0.75

Misordered Options

  • Review of misordered options:
    1. $0.75 < 70 ext{%} < 0.6 < rac{2}{3}$ - Incorrect
    2. $0.75 < 70 ext{%} < rac{2}{3} < 0.6$ - Incorrect
    3. $ rac{2}{3} < 0.6 < 70 ext{%} < 0.75$ - Incorrect
    4. $0.6 < 70 ext{%} < rac{2}{3} < 0.75$ - Incorrect
    5. $0.6 < rac{2}{3} < 70 ext{%} < 0.75$ - Correct