Comparing Whole Numbers
Learn how to compare whole numbers using place value and symbols like greater than, less than, and equal to.
Definition
- means greater than (the number on the left is larger)
- means less than (the number on the left is smaller)
- means equal to (both numbers are the same)
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Worked Examples
Compare and . Which is larger?
Count the digits in each number
has 3 digits, has 2 digits → 3 digits vs 2 digits
Apply the rule
A number with more digits is always larger (when comparing whole numbers) → has more digits
Write the comparison
→ 847 is greater than 92
Answer: because 847 has three digits while 92 has only two.
Common Mistakes
Thinking a number is larger because it has a bigger first digit, without counting digits first
Why it's wrong: For example, thinking because 9 is bigger than 1.
Correct: Always count digits first! A 3-digit number is always larger than a 2-digit number:
Confusing the direction of and symbols
Why it's wrong: Students often mix up which symbol means greater than vs less than.
Correct: The symbol always opens toward the larger number: (opens to 5) and (opens to 5)
Stopping at the first place value without checking if they are equal
Why it's wrong: If the first digits are equal, you must continue comparing to the right.
Correct: Compare left to right until you find a difference: vs — the hundreds and tens are equal, so check ones:
Interactive Visual
Place Value Chart
| Thousands 1,000 | Hundreds 100 | Tens 10 | Ones 1 |
|---|---|---|---|
| 3 | 8 | 4 | 7 |
Expanded Form:
3 × 1,000 + 8 × 100 + 4 × 10 + 7 × 1
Click on any place value to highlight it and see its value.
Click on numbers to select them. Adjust the range to explore different values.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
17 problemsWhich symbol correctly compares and ?
Why It Matters
- Shopping: Is 150 dollars more or less than your budget of 125 dollars?
- Sports: Who scored more points, the team with 87 or the team with 78?
- Time: Is 45 minutes longer or shorter than 54 minutes?
- Distance: Which city is farther, one that is 320 km away or one that is 302 km away?
Real World Applications
Population Comparison
City planners compare population numbers to allocate resources and plan infrastructure.
Example:
City A has a population of 45,800 and City B has 48,500. Since , City B is larger and may need more schools.
Three towns have populations: Town X = 12,450, Town Y = 12,540, Town Z = 12,045
Order the towns from smallest to largest population.
Step 1: Write the mathematical expression
Compare the populations using place value:
Sports Statistics
Fans and analysts compare player statistics to determine who performed better.
Example:
Player A scored 2,847 points this season. Player B scored 2,874 points. Since , Player B scored more.
Four basketball players have career points: Anna = 15,432, Ben = 15,423, Carla = 15,342, Dan = 15,324
Who has scored the most career points?
Step 1: Write the mathematical expression
Compare step by step:
Key Takeaways
- 1Compare digit count first — more digits means a larger number
- 2If digit counts are equal, compare from left to right (largest place value first)
- 3Use for greater than, for less than, for equal
- 4The comparison symbol opens toward the larger number
Frequently Asked Questions
Glossary
- Greater than
- A relationship where one number is larger than another, written with the symbol
- Less than
- A relationship where one number is smaller than another, written with the symbol
- Equal to
- A relationship where two numbers have the same value, written with the symbol
- Place value
- The value of a digit based on its position (ones, tens, hundreds, thousands, etc.)
- Digit
- A single symbol used to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9