Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
Four Similar but Different Operations
This calculator compares ways to shorten decimal numbers:
- Rounding moves to the nearest allowed value.
- Truncation simply cuts off extra digits.
- Ceiling moves upward on the number line.
- Floor moves downward on the number line.
A Simple Example
For 3.14159 to two decimal places:
| Method | Result |
|---|---|
| Round | 3.14 |
| Truncate | 3.14 |
| Ceiling | 3.15 |
| Floor | 3.14 |
Why the Method Matters
Different rules can produce different results, especially with negative numbers. A bill, laboratory report, tax rule, or display format may require a specific method, so choose the rule that matches the real task.
Frequently asked questions
Is truncation the same as rounding?
No. Truncation removes extra digits without checking what comes next, while standard rounding uses the next digit to decide whether to move up.
How are ceiling and floor different?
Ceiling moves upward on the number line; floor moves downward. With negative numbers, that is not the same as simply cutting off digits.
Why should I care about the rounding rule?
Because a report, invoice, tax rule, or measurement protocol may require one method. Using the wrong method can produce a technically incorrect result even when the difference is small.
Does the calculator round to significant figures?
No. This page rounds by decimal places. Significant-figure rounding follows a different rule because it depends on the first nonzero digit.
