Rounding Calculator
Round a number to a specified number of decimal places using standard, floor, ceil, or truncation methods. Also rounds to the nearest 10, 100, or 1000.
About this Calculator
Round a number to a specified number of decimal places using standard, floor, ceil, or truncation methods. Also rounds to the nearest 10, 100, or 1000.
Formula & Calculations
Formula
Round to d decimals: multiply by 10^d, round, divide by 10^d. Round to nearest N: round(x / N) × N.Where:
- x=The number to be rounded
- d=The number of decimal places (non-negative integer)
- Floor=The largest integer less than or equal to x
- Ceil=The smallest integer greater than or equal to x
Assumptions
- Standard rounding uses 'round half up' (0.5 rounds up).
- Floor always rounds down, ceil always rounds up.
- Truncation simply discards all digits beyond the specified decimal places.
Calculation Examples
Example 1
Standard rounding: 3.14159 → 3.14 (since the 3rd decimal is 1 < 5).
Example 2
2.71828 to 3 places: 2.718 (4th decimal is 2 < 5). Rounded to nearest 10: round(2.718/10)×10 = round(0.2718)×10 = 0.
Frequently Asked Questions
What is the difference between rounding, floor, and ceil?
Rounding goes to the nearest value (ties go up). Floor always goes down to the next lower integer. Ceil always goes up to the next higher integer. Truncation simply cuts off extra digits without rounding.
What does rounding to significant figures mean?
Significant figures round based on the magnitude of the number, not just decimal places. For example, 12345 rounded to 2 significant figures is 12000. This calculator uses decimal places, not significant figures.