Rounding Calculator
Inputs
Enter a number and choose precision to see the rounded result.
Understanding Rounding
Rounding is the process of replacing a number with an approximate value that has a shorter, simpler, or more explicit representation.
We round numbers to make them easier to work with mentally or to fit them into specific formats (like currency, which typically only uses two decimal places).
Rounding Modes
Standard Rounding (Half Up)
This is the most common method taught in schools. Look at the next digit:
- If it is 5 or more, round up.
- If it is less than 5, round down (keep it the same).
- Example: 2.5 rounds to 3. 2.4 rounds to 2.
Round Down (Floor)
Always rounds towards negative infinity. It simply chops off the extra digits.
- 2.9 rounds to 2.
- -2.1 rounds to -3.
Round Up (Ceiling)
Always rounds towards positive infinity.
- 2.1 rounds to 3.
- -2.9 rounds to -2.
Precision Levels
- Whole Number: 0 decimal places (Integer).
- Tenths: 1 decimal place (e.g., 1.2).
- Hundredths: 2 decimal places (e.g., 1.23). Common for money.
- Thousands: Rounding to the nearest 1000 (e.g., 1450 -> 1000).
Frequently Asked Questions
Why do we round?
To estimate or to simplify. Saying "the crowd was about 20,000" is easier than saying "19,843 people attended."
Is rounding checking significant figures?
Similar but slightly different. Significant figures deal with precision in measurement, whereas rounding is purely mathematical simplification.
How does rounding affect errors?
Rounding introduces a small "rounding error." In long calculations, these errors can accumulate, so it's best to only round at the very end.