Comparing Decimals

For Elementary Students

How to Compare Decimals

Comparing decimals is like comparing whole numbers, but you need to look at the place value carefully!

Think about it like this: Would you rather have $0.75 or $0.8? Let's figure it out!

The Big Mistake to Avoid

❌ WRONG thinking: "0.58 is bigger than 0.6 because 58 is bigger than 6"

✓ RIGHT thinking: Look at the place values!

Using Money to Understand

Which is more: $0.60 or $0.58?

• $0.60 = 60 cents
• $0.58 = 58 cents

60 cents is more than 58 cents!

So 0.60 > 0.58 (which is the same as 0.6 > 0.58)

The Easy Method: Add Zeros

Example: Compare 0.6 and 0.58

Step 1: Make them the same length by adding zeros

0.6  → 0.60
0.58 → 0.58

Step 2: Now compare like whole numbers!

• Look at tenths: 6 vs 5
• 6 is bigger than 5

Answer: 0.6 > 0.58 (0.6 is greater)

Another Example

Compare 0.3 and 0.29

Add zeros:

0.3  → 0.30
0.29 → 0.29

Compare:

• Tenths: 3 vs 2
• 3 is bigger!

Answer: 0.3 > 0.29

Comparing on a Number Line

0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9   1.0
|-----|-----|-----|-----|-----|-----|-----|-----|-----|
      ↑           ↑
    0.29        0.3

Numbers to the right are bigger!

For Junior High Students

The Comparison Process

Step-by-step method:

1. Line up the decimal points vertically
2. Add trailing zeros to make same length (optional but helpful)
3. Compare digit by digit from left to right
4. First different digit determines which is larger

Example 1: Basic Comparison

Compare 0.6 and 0.58

Step 1: Line up decimal points

0.6
0.58

Step 2: Add trailing zeros

0.60
0.58

Step 3: Compare place by place

• Ones place: 0 = 0 ✓
• Tenths place: 6 vs 5 → 6 is larger!

Answer: 0.6 > 0.58

Example 2: Multiple Decimal Places

Compare 3.14 and 3.2

Rewrite with same length:

3.14
3.20

Compare:

• Ones: 3 = 3 ✓
• Tenths: 1 vs 2 → 2 is larger

Answer: 3.14 < 3.2

Important: Even though 14 > 2, we must compare by place value!

Example 3: Very Close Numbers

Compare 7.305 and 7.31

Rewrite:

7.305
7.310

Compare:

• Ones: 7 = 7 ✓
• Tenths: 3 = 3 ✓
• Hundredths: 0 vs 1 → 1 is larger

Answer: 7.305 < 7.31

Comparing Whole Number Parts First

Always compare the whole number part before the decimal part!

Example: Compare 4.9 and 5.1

• Whole numbers: 4 vs 5
• 5 is bigger, so 4.9 < 5.1

(Don't even need to look at decimal parts!)

Common Mistakes

Mistake 1: Thinking more digits means larger

❌ "0.125 > 0.9 because 125 > 9"

✓ 0.125 < 0.9 (compare: 0.125 vs 0.900)

Mistake 2: Ignoring place value

❌ Comparing "58" vs "6" instead of comparing 0.58 vs 0.60

✓ Always align decimal points first!

Mistake 3: Forgetting the whole number part

❌ Thinking 2.9 > 3.1 because 9 > 1

✓ Look at whole numbers first: 2 < 3, so 2.9 < 3.1

Ordering Multiple Decimals

Example: Order from smallest to largest: 0.4, 0.38, 0.41

Step 1: Rewrite with same length

0.40
0.38
0.41

Step 2: Compare

• All have 0 ones
• Tenths: all have 3 or 4
  • 0.38 (tenths = 3)
  • 0.40 (tenths = 4, hundredths = 0)
  • 0.41 (tenths = 4, hundredths = 1)

Step 3: Order from smallest to largest

Answer: 0.38, 0.4, 0.41

Using Symbols

> means "greater than"

• 0.8 > 0.7 (0.8 is greater than 0.7)

< means "less than"

• 0.3 < 0.5 (0.3 is less than 0.5)

= means "equal to"

• 0.7 = 0.70 (same value)

Memory trick: The open mouth eats the bigger number!

Comparing Decimals with Fractions

Example: Which is larger: 0.5 or 3/4?

Convert to same form:

• 0.5 = 5/10 = 1/2
• 3/4 = 0.75

Compare: 0.50 vs 0.75 → 0.75 is larger

Answer: 3/4 > 0.5

Real-Life Applications

Shopping: "Is $3.49 or $3.95 cheaper?" → $3.49

Measurements: "Is 0.75 inches or 0.8 inches longer?" → 0.8 inches

Sports: "Who ran faster: 10.5 seconds or 10.48 seconds?" → 10.48 seconds (smaller time = faster)

Grades: "Is 89.7% or 90.1% higher?" → 90.1%

Quick Comparison Tricks

Same tenths? Look at hundredths

• 0.47 vs 0.43 → Both have 4 tenths, but 7 > 3 hundredths

Same whole number? Look at tenths

• 5.8 vs 5.3 → Both are 5 point something, but 8 > 3 tenths

Different whole numbers? Whole number wins!

• 3.99 vs 4.01 → 4 > 3, so 4.01 is larger

Practice