If the digit is 5 or greater (5, 6, 7, 8, 9):
Round UP ⬆️
If the digit is less than 5 (0, 1, 2, 3, 4):
Round DOWN ⬇️
This is the fundamental rounding rule taught in schools worldwide. Also known as "round half up" or "standard rounding," it's used in most mathematical and everyday applications.
3.5 → 4 (5 rounds up)
3.6 → 4 (6 rounds up)
3.7 → 4 (7 rounds up)
3.8 → 4 (8 rounds up)
3.9 → 4 (9 rounds up)
3.0 → 3 (0 rounds down)
3.1 → 3 (1 rounds down)
3.2 → 3 (2 rounds down)
3.3 → 3 (3 rounds down)
3.4 → 3 (4 rounds down)
Look at the ones digit:
23 → 20 (3 < 5, round down)
27 → 30 (7 ≥ 5, round up)
45 → 50 (5 = 5, round up)
Look at the tens digit:
234 → 200 (3 < 5, round down)
567 → 600 (6 ≥ 5, round up)
850 → 900 (5 = 5, round up)
Look at the hundredths digit:
3.14 → 3.1 (4 < 5, round down)
3.17 → 3.2 (7 ≥ 5, round up)
3.15 → 3.2 (5 = 5, round up)
Look at the thousandths digit:
3.142 → 3.14 (2 < 5, round down)
3.147 → 3.15 (7 ≥ 5, round up)
3.145 → 3.15 (5 = 5, round up)
When the digit is exactly 5, round to the nearest even number. This reduces bias in statistical calculations.
2.5 → 2 (round to even)
3.5 → 4 (round to even)
4.5 → 4 (round to even)
5.5 → 6 (round to even)
Used in: Banking, statistics, IEEE 754 floating-point standard, Python's round()
When the digit is exactly 5, round DOWN. Less common but used in specific applications.
2.5 → 2
3.5 → 3
4.5 → 4
Always round UP to the next value, regardless of the digit.
3.1 → 4
3.5 → 4
3.9 → 4
Used in: Inventory (can't order 0.7 boxes), staffing, project planning
Always round DOWN, removing all decimals (truncate).
3.1 → 3
3.5 → 3
3.9 → 3
Used in: Age calculations, completed years, conservative estimates
| Rounding Rule | When to Use | Example |
|---|---|---|
| Standard (5 up) | General math, school, everyday use | Test scores, measurements |
| Bankers' Rounding | Statistics, banking, reduce bias | Financial calculations |
| Always Up (Ceiling) | Inventory, staffing, materials | 47.3 boxes → 48 boxes |
| Always Down (Floor) | Age, years of service | 12.9 years old → 12 years |
Wrong: To round 347 to the nearest hundred, looking at the 4
Right: Look at the tens digit (4), which tells you to round down to 300
Wrong: Round 3.456 → 3.46 → 3.5 (double rounding changes the result!)
Right: Round 3.456 → 3.5 directly (one-step rounding)
Wrong: Thinking 2.5 rounds down to 2
Right: 2.5 rounds UP to 3 (in standard rounding)
Wrong: Round intermediate values during calculations (loses precision)
Right: Keep full precision, only round the final answer
5+ goes UP ⬆️
<5 goes DOWN ⬇️
Look at the digit RIGHT AFTER the place you're rounding to
Check the ones digit
27 → 30
Check the tens digit
567 → 600
Check the hundredths
3.17 → 3.2
Check the thousandths
3.147 → 3.15