Comparing Decimals – Greater, Less, or Equal?
Comparing decimals means deciding which of two (or more) decimal numbers is greater, smaller, or equal. It is a vital skill for checking prices, measurements, and data.
Why Comparing Can Seem Tricky
People sometimes think 0.9 is smaller than 0.15 because 9 is less than 15. This is wrong. To compare correctly, you must look at each place value column in order, starting from the largest.
The Golden Rule
Line up the decimal points. Then compare digit by digit, from left to right, stopping as soon as one digit is larger than the other.
Step-by-Step Method
Ones: both have 3 — equal so far.
Tenths: 4 vs 5 — 5 is larger.
So 3.52 is greater than 3.47. Write: 3.47 < 3.52.
Ones: both 0 — equal.
Tenths: 9 vs 1 — 9 is larger.
So 0.9 is greater. Write: 0.9 > 0.15.
5.4 = 5.40 because trailing zeros do not change value. Write: 5.4 = 5.40.
Using the Symbols
| Symbol | Meaning | Example |
|---|---|---|
| < | Is less than | 2.3 < 2.7 |
| > | Is greater than | 0.9 > 0.15 |
| = | Is equal to | 0.50 = 0.5 |
Adding Zeros to Help
You can always add trailing zeros to make the decimals the same length before comparing.
Write 1.3 as 1.300.
Compare 1.300 and 1.275.
Ones: 1 = 1. Tenths: 3 > 2. So 1.3 > 1.275.
Common Mistakes
0.15 has more digits than 0.9. But 0.9 is bigger. Always compare by place value, not by number of digits.
0.30 and 0.3 are the same. But 0.03 is ten times smaller than 0.3. Watch where the zeros fall.
Key Takeaways
- Compare decimal by decimal place, starting with the largest (leftmost) column.
- Adding trailing zeros does not change value but makes comparison easier.
- More decimal digits does not mean a larger number.
- Use <, >, and = to record your comparison.
Practice Questions
- Write < or > between each pair: 0.7 _ 0.70; 3.45 _ 3.5; 0.09 _ 0.1
- Which is greater: 4.08 or 4.8?
- A sprinter runs 100 m in 10.42 seconds. Another runs it in 10.39 seconds. Who is faster?
- Compare 0.005 and 0.05.
- Order these from least to greatest: 2.3, 2.03, 2.33, 2.003.