Comparing and Ordering Numbers

Comparing Two Numbers

Comparing means figuring out which number is bigger or if they're equal.

We use three symbols:

• > means "greater than" (bigger)
• < means "less than" (smaller)
• = means "equal to" (the same)

Memory trick: The symbol opens to the BIGGER number, like an alligator mouth eating the bigger number!

Steps to Compare Numbers

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

• Thousands: Both have 5 ✓ (same)
• Hundreds: One has 8, the other has 7 → 8 > 7!
• Since 8 > 7, we know: 5,847 > 5,792 ✓

Comparing Different-Sized Numbers

Quick rule: If numbers have different amounts of digits, the one with MORE digits is bigger!

Examples:

• 9,999 < 10,000 (4 digits vs 5 digits)
• 999,999 < 1,000,000 (6 digits vs 7 digits)
• 45 < 100 (2 digits vs 3 digits)

Using Place Value to Compare

Always compare the highest place value first:

56,432 vs 56,891

• Ten thousands: 5 = 5 ✓
• Thousands: 6 = 6 ✓
• Hundreds: 4 vs 8 → 4 < 8
• Answer: 56,432 < 56,891

Ordering Numbers (Least to Greatest)

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 ✓

Greatest to Least

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

Using a Number Line

Number lines help visualize comparisons. Numbers to the RIGHT are always bigger!

Example: Comparing 325 and 867

Think of a number line from 0 to 1,000:

0 ————————— 250 ————————— 500 ————————— 750 ————————— 1,000
              ↑                                  ↑
            325                                867

Since 867 is to the right of 325, we know: 867 > 325 ✓

Key points about number lines:

• Numbers get larger as you move right →
• Numbers get smaller as you move left ←
• The farther right, the bigger the number!
• The farther left, the smaller the number!

Comparing with Zeros

Don't forget about zeros!

234 vs 204:

• Hundreds: 2 = 2 ✓
• Tens: 3 vs 0 → 3 > 0
• Answer: 234 > 204

Leading zeros don't matter:

• 0,567 = 567
• 00,045 = 45

Real-World Applications

Money: Which is more: $4,567 or $4,756?

• Compare: 5 hundreds vs 7 hundreds
• $4,756 is more! ✓

Distances: Which is farther: 12,405 miles or 12,450 miles?

• Compare: 0 tens vs 5 tens
• 12,450 miles is farther! ✓

Scores: Order these game scores: 89,540 | 89,450 | 98,540

• Greatest: 98,540 (biggest ten-thousands)
• Middle: 89,540 (next)
• Least: 89,450

Practice Strategy

Use this checklist:

1. ☐ Count the digits (more = bigger)
2. ☐ Line up by place value
3. ☐ Start comparing from the left
4. ☐ Stop at the first different digit
5. ☐ Use >, <, or = correctly

Remember the symbols:

• 5 < 8 means "5 is less than 8"
• 8 > 5 means "8 is greater than 5"
• The arrow points to the smaller number!

Common Mistakes

❌ 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!