Comparing Decimals
Which is greater? Which is less? Are they equal?
🔑 Key Strategy
Place value is everything!
Students often think 0.15 > 0.8 because "15 is bigger than 8"
But that's wrong! We can't just compare the digits — we need to look at place value.
Always compare digits in the same place value position!
- Start at the left (biggest place value)
- Compare digit by digit, moving right
- The first difference tells you which is greater
📏 Strategy 1: Line Up the Decimals
Compare 0.7 and 0.52
| Ones | . | Tenths | Hundredths |
|---|---|---|---|
| 0 | . | 7 | 0 |
| 0 | . | 5 | 2 |
The tenths place is different: 7 > 5
So 0.7 > 0.52 ✓
Add zeros to make the decimals the same length: 0.7 = 0.70
Now it's easy to see: 0.70 vs 0.52 — which is bigger?
💰 Strategy 2: Think Money!
Which is greater: 0.25 or 0.3?
30¢ > 25¢, so 0.3 > 0.25 ✓
0.3 is the same as $0.30 (thirty cents)
0.03 is the same as $0.03 (three cents)
Big difference! 30¢ ≠ 3¢
🔄 Strategy 3: Equivalent Decimals
0.5 = 0.50 = 0.500
Adding zeros after the last digit doesn't change the value
Leading zeros DO change the value:
0.5 ≠ 0.05 ≠ 0.005
50¢ ≠ 5¢ ≠ half a penny!
📍 Strategy 4: Number Line
Where do decimals fall on a number line?
0.3
0.15
Numbers further RIGHT are GREATER
0.3 is to the right of 0.15, so 0.3 > 0.15
✏️ Problem 1
Compare the decimals
Which symbol goes in the blank: >, <, or =?
Line up the decimals: 0.80 vs 0.35
Compare tenths: 8 tenths > 3 tenths
💰 Money check: 80¢ vs 35¢ — 80¢ is more!
✏️ Problem 2
Compare the decimals
Line up the decimals: 0.09 vs 0.60
Compare tenths: 0 tenths < 6 tenths
💰 Money check: 9¢ vs 60¢ — 9¢ is way less!
⚠️ Don't be tricked! 9 looks bigger than 6, but place value matters!
✏️ Problem 3
Compare the decimals
These are equivalent decimals!
0.70 = 0.7 (the trailing zero doesn't change the value)
💰 Money check: 70¢ = 70¢ ✓
✏️ Problem 4
Compare the decimals
Line up the decimals: 0.125 vs 0.200
Compare tenths: 1 tenth < 2 tenths
We already know! No need to look further.
⚠️ Don't be tricked by "125 vs 2" — place value matters!
🤔 Problem 5: Who Is Correct?
Do you agree with Marcus?
No, Marcus is incorrect!
Marcus made a common mistake — he compared 19 to 3 without thinking about place value.
Let's line them up:
| Ones | . | Tenths | Hundredths |
|---|---|---|---|
| 0 | . | 1 | 9 |
| 0 | . | 3 | 0 |
The tenths place: 1 < 3, so 0.19 < 0.3
💰 Think: 19¢ < 30¢
🤔 Problem 6: Who Is Correct?
Do you agree with Sofia?
Yes, Sofia is correct!
These are equivalent decimals.
Adding zeros after the last digit doesn't change the value:
0.5 = 0.50 = 0.500
💰 Think: 50¢ = 50¢ = 50¢ ✓
All three represent five tenths or half of one.
🤔 Problem 7: Who Is Correct?
Do you agree with Aiden?
No, Aiden is incorrect!
The position of the digits matters, not just which digits they are!
| Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 0 | . | 3 | 0 | 0 |
| 0 | . | 0 | 0 | 3 |
0.300 = 3 tenths = 30¢
0.003 = 3 thousandths = less than 1¢
✏️ Problem 8
Compare the decimals
Line up the decimals: 0.450 vs 0.405
Compare tenths: 4 = 4 ✓ (same)
Compare hundredths: 5 > 0
The hundredths place decides it!
✏️ Problem 9
Compare the decimals
Line up the decimals: 0.062 vs 0.620
Compare tenths: 0 < 6
💰 Think: about 6¢ vs 62¢ — big difference!
⚠️ That leading zero in 0.062 makes a huge difference!
⚖️ Problem 10: True or False?
TRUE!
0.8 = 0.80, which is greater than 0.75
💰 Think: 80¢ > 75¢ ✓
⚖️ Problem 11: True or False?
FALSE!
Line up: 0.099 vs 0.100
Tenths: 0 < 1
💰 Think: about 10¢ vs 10¢... actually 9.9¢ < 10¢
⚠️ 99 looks bigger than 1, but place value rules!
⚖️ Problem 12: True or False?
FALSE!
0.40 = 4 tenths = 40¢
0.04 = 4 hundredths = 4¢
💰 40 cents is NOT equal to 4 cents!
The position of the 4 completely changes the value.
📊 Problem 13: Put in Order
Least to Greatest
Line them up: 0.50, 0.05, 0.55
💰 Think money: 50¢, 5¢, 55¢
0.05 (5¢) is the smallest
0.5 (50¢) is in the middle
0.55 (55¢) is the largest
📊 Problem 14: Put in Order
Least to Greatest
Line them up: 0.400, 0.420, 0.402, 0.240
Compare tenths first: 0.24 has 2 tenths (smallest!)
The other three all have 4 tenths — compare hundredths:
• 0.400 → 0 hundredths
• 0.402 → 0 hundredths (but has 2 thousandths)
• 0.420 → 2 hundredths (largest!)
✏️ Problem 15
Compare the decimals
Line them up: 0.909 vs 0.910
Tenths: 9 = 9 ✓
Hundredths: 0 < 1
The hundredths place decides it!
🤔 Problem 16: Who Is Correct?
Do you agree with Mia?
No, Mia is incorrect! (And her reasoning is backward!)
Let's check:
• 0.72 = 72 hundredths = 72¢
• 0.6 = 60 hundredths = 60¢
72¢ > 60¢, so 0.72 > 0.6
Being "closer to 1" actually means the number is GREATER!
✏️ Problem 17
Compare the decimals
These are equivalent decimals!
The trailing zero in 0.250 doesn't change the value.
💰 Both equal 25¢ (a quarter!)
📊 Problem 18: Put in Order
Greatest to Least
Line them up: 0.800, 0.080, 0.880, 0.808
💰 Think money: 80¢, 8¢, 88¢, about 81¢
0.88 (88¢) is the greatest
0.808 (about 81¢) is second
0.8 (80¢) is third
0.08 (8¢) is the least
🎉 Great Work!
Key Takeaways
- Line up decimal points
- Compare place by place (left to right)
- Add zeros to make same length
- Think about money!
- ✗ Compare digits without place value
- ✗ Think "more digits = bigger"
- ✗ Ignore where zeros are located
- ✗ Compare 19 to 3 directly
🧠 Remember
Place value is EVERYTHING!