Rounding Calculator
Round numbers to specified decimal places. Shows rounded, floor, ceiling, and truncated values. See also Significant Figures Calculator and Decimal to Fraction.
How to Round Numbers
Rounding replaces a number with an approximate value that has fewer digits. Look at the digit immediately after your desired precision: if it is 5 or greater, round up; if it is less than 5, round down. Floor always rounds toward negative infinity, ceiling always rounds toward positive infinity, and truncation simply removes digits beyond the specified place.
Rounding Rules
Round half up (standard):
If digit ≥ 5 → round up
If digit < 5 → round down
Floor: always round toward −∞
Ceiling: always round toward +∞
Truncate: remove digits (round toward 0)
Example
Number: 3.14159
Round to 2 decimal places:
Rounded: 3.14 (digit after is 1, which is < 5)
Floor: 3.14
Ceiling: 3.15
Truncated: 3.14
Frequently Asked Questions
What is the difference between rounding and truncating?
Rounding considers the next digit to decide whether to go up or down. Truncating simply removes all digits beyond the specified place, always moving toward zero.
What happens when the digit is exactly 5?
Standard rounding (round half up) rounds 5 upward. Some systems use "round half to even" (banker's rounding) which rounds to the nearest even number to reduce bias.
How do floor and ceiling differ for negative numbers?
Floor rounds toward negative infinity (e.g., floor(−2.3) = −3), while ceiling rounds toward positive infinity (e.g., ceil(−2.3) = −2). Truncation rounds toward zero (e.g., trunc(−2.3) = −2).
Solved Examples — Rounding Numbers
Example: Round 47,863 to the nearest thousand
Solution:
Step 1: The thousands digit is 7 (47,863)
Step 2: Look at the hundreds digit: 8 (≥ 5, so round up)
Step 3: Increase thousands digit: 7 → 8, replace remaining with zeros
Answer: 48,000
Example: Round 0.08647 to 3 decimal places
Solution:
Step 1: Keep first 3 decimal digits: 0.086...
Step 2: Look at 4th decimal digit: 4 (< 5, so round down)
Step 3: Keep 6 as-is
Answer: 0.086
Example: A store prices items at $14.95. How much is it rounded to the nearest dollar?
Solution:
Step 1: Round to 0 decimal places
Step 2: Look at first decimal digit: 9 (≥ 5, round up)
Step 3: 14 → 15
Answer: $15
Practice Questions
Try these on your own:
- Round 3.7521 to 2 decimal places (Answer: 3.75)
- Round 845 to the nearest hundred (Answer: 800)
- Round −2.65 to 1 decimal place using round-half-up (Answer: −2.6)
- What is floor(7.9)? (Answer: 7)
- What is ceiling(−3.2)? (Answer: −3)
- Round 2,549,500 to the nearest million (Answer: 3,000,000)
Common Mistakes to Avoid
The most common mistake is "chain rounding" — rounding in multiple steps instead of once. For example, rounding 2.449 to 1 decimal place: if you first round to 2.45, then to 2.5, you get the wrong answer. The correct single-step result is 2.4 (since the digit after the first decimal is 4). Another error is confusing floor with truncation for negative numbers: floor(−2.3) = −3, but truncate(−2.3) = −2. Students also sometimes round the wrong digit — always look at the digit AFTER the place you're rounding to, not the digit itself. When rounding to a specific place value (like nearest hundred), all digits to the right become zero. Also, 5 always rounds UP in standard rounding (round-half-up), not towards the nearest even number (unless using banker's rounding).
Key Takeaways
- Standard rounding: look at the digit immediately after the rounding position. ≥ 5 rounds up, < 5 rounds down.
- Floor always rounds toward −∞ (down for positives, more negative for negatives).
- Ceiling always rounds toward +∞ (up for positives, less negative for negatives).
- Truncation removes digits and rounds toward zero (different from floor for negatives).
- Never chain-round — always round in a single step from the original number.
- Rounding is used everywhere: currency (2 decimals), statistics, measurements, and estimation.