Lecture on Comparing and Ordering Decimals

Key Concepts

• Comparing Decimals: Determining if one decimal is greater than, less than, or equal to another.
• Ordering Decimals: Arranging decimals from least to greatest or vice versa.

Strategies for Comparing and Ordering Decimals

1. Visual Representation:
   • Draw pictures to compare the shaded area in decimal grids.
2. Number Line:
   • Place decimals on a number line to visually see their order.
3. Place Value Comparison:
   • Write decimals in a column format to compare digit by digit using place value.

Examples

Example 1: Comparing Decimals

• Decimals: 8/10 and 6/10
  • By drawing, 8/10 has more shaded area than 6/10.
  • Conclusion: 8/10 is greater than 6/10.

Example 2: Comparing Decimals with Different Denominators

• Decimals: 4/10 and 17/100
  • Concept: Tenths are bigger than hundredths (like dimes vs. pennies).
  • By drawing, 4/10 fills more space than 17/100.
  • Conclusion: 4/10 is greater than 17/100.

Example 3: Ordering Three Decimals

• Decimals: 2/10, 27/100, 19/100
  • Using a number line:
    • 2/10 = 20/100, plotted at 20
    • 27/100, plotted at 27
    • 19/100, plotted at 19
  • Order from least to greatest: 19/100, 2/10, 27/100.

Example 4: Different Strategy for Three Decimals

• Decimals: 63/100, 6/10, 71/100
  • Align decimals vertically and compare place values.
  • Result:
    • Greatest: 71/100
    • Middle: 63/100
    • Least: 6/10

Practice Problems

• Problem 1: Compare 4/10 and 32/100
  • Answer: 4/10 is greater than 32/100
• Problem 2: Order from least to greatest
  • Decimals: 34/100, 3/10, 37/100
  • Answer: 3/10, 34/100, 37/100

Homework

• Compare and order these decimals:
  1. Is 2/10 or 27/100 greater?
  2. Is 86/100 or 9/10 greater?
  3. Order 43/100, 51/100, and 5/10 from least to greatest.
  4. Order 2/10, 17/100, and 32/100 from least to greatest.

Bring your answers to class tomorrow for review.