Comparing Numbers
Comparing numbers means deciding which of two (or more) numbers is greater, which is smaller, or whether they are equal. This skill is used whenever you order lists, choose the best value, or solve inequalities in algebra.
Comparison Symbols
| Symbol | Meaning | Example |
|---|---|---|
| > | Greater than | 7 > 3 |
| < | Less than | 3 < 7 |
| = | Equal to | 5 = 5 |
Comparing Whole Numbers – Step by Step
- Count the digits. The number with more digits is larger.
- If digit counts are equal, compare the leftmost digits.
- Move right until you find digits that differ.
- The number with the larger digit in that position is greater.
Worked Examples
| Comparison | Reason | Result |
|---|---|---|
| 5,821 vs 5,279 | Thousands equal (5=5); hundreds: 8 > 2 | 5,821 > 5,279 |
| 74,000 vs 6,999 | 74,000 has 5 digits; 6,999 has 4 | 74,000 > 6,999 |
| 302 vs 302 | All digits identical | 302 = 302 |
| 1,050 vs 1,500 | Thousands equal; hundreds: 0 < 5 | 1,050 < 1,500 |
Comparing Decimals
- Compare the whole number parts first.
- If equal, compare tenths, then hundredths, and so on.
3.74 vs 3.79 → ones equal, tenths equal (7=7), hundredths: 4 < 9 → 3.74 < 3.79
Using a Number Line
On a number line, numbers increase from left to right. Any number to the right is greater than any number to the left.
← 0 1 2 3 4 5 6 7 8 9 10 →
Comparing Negative Numbers
Negative numbers are to the left of zero on a number line. The further left, the smaller the value.
−5 < −2 (because −5 is further left)
Key Points
- More digits always means a larger number (for positive whole numbers).
- Compare digit by digit from left to right.
- For decimals, align decimal points before comparing.
- Negative numbers: the larger the absolute value, the smaller the number.
Quick Practice
- Compare 45,632 and 45,723 using >, < or =.
- Which is greater: 0.085 or 0.1?
- Arrange in ascending order: 3,410; 3,041; 3,401.
- Insert the correct symbol: −8 __ −3.
- True or false: 999,999 > 1,000,000.
Summary
Comparing numbers relies entirely on place value: more digits means a larger number, and when digit counts match, you compare position by position from left to right. The skill extends naturally to decimals and negative numbers, and is essential for ordering, rounding, and solving inequalities.