Comparing & Ordering Numbers
Using symbols to compare, ordering from smallest to largest, and rounding large numbers
1. Comparing Large Numbers
Comparison Symbols
<
Less than
smaller number first
>
Greater than
bigger number first
=
Equal to
same value
💡 Memory Trick: The Hungry Crocodile!
Think of < and > as a crocodile's mouth. The crocodile is hungry and always wants to eat the bigger number!
Steps to Compare Large Numbers:
- First, check the number of digits - for whole numbers, more digits = bigger number
- If they have the same number of digits, compare from the left (biggest place value first)
- Find the first digit that's different
- The number with the bigger digit wins!
Example: Compare 3,456,789 and 3,465,123
| Number | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|---|
| 3,456,789 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 3,465,123 | 3 | 4 | 6 | 5 | 1 | 2 | 3 |
Same digits until the ten thousands place: 5 < 6
Therefore: 3,456,789 < 3,465,123
2. Ordering Numbers
Two Ways to Order:
Ascending Order
Smallest → Largest
Going UP like climbing stairs
1 → 2 → 3 → 4 → 5
Descending Order
Largest → Smallest
Going DOWN like a slide
5 → 4 → 3 → 2 → 1
Example: Order 2,345,000 | 2,340,500 | 2,345,001 in ascending order
Step 1: All have 7 digits, so compare from left
Step 2: All start with 2,34...
Compare the 4th digit (thousands):
- 2,340,500 → 0
- 2,345,000 → 5
- 2,345,001 → 5
Step 3: 2,340,500 is smallest (0 in thousands)
Compare 2,345,000 and 2,345,001:
Ones place: 0 vs 1 → 2,345,000 is smaller
Ascending order:
2,340,500 < 2,345,000 < 2,345,001
3. Rounding Large Numbers
Rounding Rules:
Look at the digit one place to the right of where you're rounding to:
- If it's 0, 1, 2, 3, or 4 → Round DOWN (keep the digit the same)
- If it's 5, 6, 7, 8, or 9 → Round UP (add 1 to the digit; if that digit is 9, it becomes 0 and the digit on its left goes up by 1, as in 3,960,000 → 4,000,000 to the nearest hundred thousand)
Then change all digits to the right to zeros!
Rounding Examples for 3,456,789:
Round to nearest 10: 3,456,789
Ones digit 9 is 5 or more, so round up → 3,456,790
Round to nearest 1,000: 3,456,789
Hundreds digit 7 is 5 or more, so round up → 3,457,000
Round to nearest 100,000: 3,456,789
Ten thousands digit 5 is 5 or more, so round up → 3,500,000
Round to nearest million: 3,456,789
Hundred thousands digit 4 is less than 5, so round down → 3,000,000
Example: Round 7,849,521 to the nearest hundred thousand
Step 1: Find the hundred thousands digit: 7,849,521 → 8
Step 2: Look at the digit to its right (ten thousands): 7,849,521 → 4
Step 3: 4 < 5, so round DOWN (keep the 8)
Answer: 7,800,000
Example: Round 4,950,000 to the nearest million
Step 1: Find the millions digit: 4,950,000 → 4
Step 2: Look at the digit to its right (hundred thousands): 4,950,000 → 9
Step 3: 9 is 5 or more, so round UP (4 becomes 5)
Answer: 5,000,000
Practice Problems
1. Compare using <, >, or =
a) 5,234,567 ___ 5,243,567
b) 8,000,001 ___ 7,999,999
c) 3,500,000 ___ 3,500,000
ShowHide solutions
a) 5,234,567 < 5,243,567 (3 < 4 in ten thousands)
b) 8,000,001 > 7,999,999 (8 > 7 in millions)
c) 3,500,000 = 3,500,000 (same number)
2. Arrange in descending order:
4,567,890 | 4,576,890 | 4,567,980 | 4,567,809
ShowHide solution
Descending (largest to smallest):
4,576,890 > 4,567,980 > 4,567,890 > 4,567,809
3. Round 6,385,472 to:
a) Nearest ten thousand
b) Nearest hundred thousand
c) Nearest million
ShowHide solutions
a) 6,390,000 (5 in thousands, so round up)
b) 6,400,000 (8 in ten thousands, so round up)
c) 6,000,000 (3 in hundred thousands, so round down)
Key Takeaways
- < means less than, > means greater than, = means equal to
- Compare from the left (biggest place value first)
- Ascending = smallest to largest (going up)
- Descending = largest to smallest (going down)
- When rounding, look at the digit one place to the right
- Digits 0-4 → round down, Digits 5-9 → round up
- After rounding, replace all digits to the right with zeros