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Compare and order multi-digit numbers
Learn step-by-step with practice exercises built right in.
Comparing means figuring out which number is bigger or if they're equal.
We use three symbols:
Memory trick: The symbol opens to the BIGGER number, like an alligator mouth eating the bigger number!
1. Line up the numbers by place value 2. Start from the LEFT (biggest place) 3. Compare digit by digit 4. The first different digit tells you which is bigger
Example: Compare 5,847 and 5,792
5,847
5,792
Compare using <, >, or =: 5,678 ___ 5,876
Compare digit by digit from left to right:
5,678 5,876
Thousands: 5 = 5 ✓ Hundreds: 6 < 8 ← Different!
Since 6 < 8, we know:
5,678 < 5,876 ✓
5,678 is less than 5,876
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Quick rule: If numbers have different amounts of digits, the one with MORE digits is bigger!
Examples:
Always compare the highest place value first:
56,432 vs 56,891
Ordering means arranging numbers from smallest to largest (or largest to smallest).
Example: Order these: 4,521 | 4,215 | 4,512
Step 1: Compare all the numbers Step 2: Find the smallest Step 3: Find the next smallest Step 4: Continue until done
All have 4 thousands, so compare hundreds:
- 4,521 has 5 hundreds
- 4,215 has 2 hundreds (smallest!)
- 4,512 has 5 hundreds
For the two with 5 hundreds, compare tens:
- 4,521 has 2 tens
- 4,512 has 1 ten (this one is next!)
Final order: 4,215 < 4,512 < 4,521 ✓
Same process, but arrange from biggest to smallest!
Example: Order from greatest to least: 892, 8,920, 89
Step 1: Find the biggest (most digits): 8,920
Step 2: Find the next: 892
Step 3: What's left: 89
Answer: 8,920 > 892 > 89
Number lines help visualize comparisons:
0 ―――――― 250 ―――――― 500 ―――――― 750 ―――――― 1,000
↑ ↑
325 867
Numbers to the RIGHT are bigger! So 867 > 325
Don't forget about zeros!
234 vs 204:
Leading zeros don't matter:
Money: Which is more: 4,756?
Distances: Which is farther: 12,405 miles or 12,450 miles?
Scores: Order these game scores: 89,540 | 89,450 | 98,540
Use this checklist:
Remember the symbols:
❌ Comparing from the right instead of left ❌ Thinking more digits always means bigger (0,005 is NOT bigger than 5!) ❌ Forgetting to line up place values ❌ Getting < and > confused
✅ Always start from the LEFT (highest place value) ✅ The number with more digits is usually bigger ✅ Make sure place values line up ✅ The symbol "eats" the bigger number!
Order from least to greatest: 34,567 34,765 34,576
Compare digit by digit:
34,567 34,765 34,576
All have 34 in the thousands → compare hundreds:
Two have 5 hundreds, one has 7 hundreds. For the two with 5 hundreds, compare tens:
Order from least to greatest: 34,567 < 34,576 < 34,765 ✓
Which is greatest: 98,999 or 100,001?
Compare the number of digits first:
98,999 → 5 digits 100,001 → 6 digits
A 6-digit number is always greater than a 5-digit number!
100,001 is greatest ✓
Even though 98,999 has mostly 9s, 100,001 is bigger because it has an extra digit in the hundred thousands place.
Order from greatest to least: 7,200 7,020 7,002 7,220
Compare digit by digit:
All start with 7 thousands → compare hundreds:
The two with 2 hundreds are bigger. For those two, compare tens:
7,220 is biggest!
For the two with 0 hundreds, compare tens:
Order from greatest to least: 7,220 > 7,200 > 7,020 > 7,002 ✓
True or False: A number with more digits is always greater.
TRUE! ✓
A number with more digits is ALWAYS greater than a number with fewer digits.
Examples:
This is the FIRST thing to check when comparing numbers!
If the numbers have the same number of digits, THEN you compare digit by digit from left to right.