MathIsimple
Lesson 3-2

Decimal Comparison & Ordering

Learn to compare and order decimals using place value understanding. Master decimal comparison with race times and real-world scenarios.

Learning Scenario: Race Times Comparison

Scenario: You're timing a 100-meter race! The runners' times are: Alex 12.4 seconds, Sarah 12.35 seconds, and Mike 12.8 seconds. Who finished first, second, and third? How do you determine the order when the times are so close?

This is where decimal comparison skills come in handy! We need to compare decimals by looking at each place value from left to right to determine which is larger or smaller.

Comparing Decimals

Compare decimals by looking at each place value from left to right, starting with the largest place value.

Steps:

  1. 1. Compare whole number parts first
  2. 2. If equal, compare tenths place
  3. 3. If equal, compare hundredths place
  4. 4. Continue until you find a difference
Ordering Decimals

To order decimals, arrange them from smallest to largest (ascending) or largest to smallest (descending).

Example:

Ascending: 0.5, 0.05, 0.55 → 0.05, 0.5, 0.55

Descending: 0.5, 0.05, 0.55 → 0.55, 0.5, 0.05

Step-by-Step Learning
1

Compare Whole Number Parts

Start by comparing the digits to the left of the decimal point. The number with the larger whole number part is greater.

Example: 3.7 vs 2.9 → 3 > 2, so 3.7 > 2.9

2

Compare Tenths Place

If the whole number parts are equal, compare the tenths place (first digit after the decimal point).

Example: 2.4 vs 2.7 → 4 < 7, so 2.4 < 2.7

3

Compare Hundredths Place

If the tenths are also equal, compare the hundredths place (second digit after the decimal point).

Example: 2.45 vs 2.43 → 5 > 3, so 2.45 > 2.43

Interactive Activities

Activity 1: Race Time Ordering

Order these race times from fastest to slowest:

  • • 12.4 seconds
  • • 12.35 seconds
  • • 12.8 seconds
  • • 12.05 seconds
  • • 12.45 seconds

Activity 2: Decimal Sorting

Sort these decimals from smallest to largest:

  • • 0.5, 0.05, 0.55
  • • 1.23, 1.2, 1.203
  • • 3.7, 3.07, 3.70
  • • 0.9, 0.09, 0.99
Practice Problems

Problem Set 1: Comparison

1. 0.7 ___ 0.07 (>, <, or =)

2. 2.45 ___ 2.54 (>, <, or =)

3. 1.23 ___ 1.203 (>, <, or =)

4. 0.9 ___ 0.90 (>, <, or =)

Problem Set 2: Ordering

5. Order from smallest to largest: 0.6, 0.06, 0.66

6. Order from largest to smallest: 1.5, 1.05, 1.55

7. Order from smallest to largest: 2.3, 2.03, 2.33

8. Order from largest to smallest: 0.8, 0.08, 0.88

Problem Set 3: Real-World Applications

9. Which is heavier: 2.5 kg or 2.05 kg?

10. Which is longer: 1.25 m or 1.2 m?

11. Which temperature is higher: 23.5°C or 23.05°C?

12. Which price is lower: $12.99 or $12.9?

Common Mistakes to Avoid

❌ Comparing by number of digits

Wrong: 0.5 < 0.05 because 0.05 has more digits

Correct: 0.5 > 0.05 because 5 tenths > 5 hundredths

❌ Ignoring place values

Wrong: 1.23 = 1.203 because both have 1, 2, and 3

Correct: 1.23 > 1.203 because 3 tenths > 0 tenths

Key Takeaways

Compare decimals by place value from left to right

Start with the largest place value and work your way down

Use number lines to visualize decimal order

Practice with real-world examples like measurements and money