Round to nearest, up or down.
rounded = floor(N × 10^d + 0.5) / 10^d
To round a number N to d decimal places, multiply N by 10^d, apply the floor function plus 0.5, then divide back by 10^d. This implements the standard "round half up" rule (halves round away from zero for positive numbers).
Step 1: Multiply by 10^2 = 100 → 3.14159 × 100 = 314.159 Step 2: Add 0.5 → 314.159 + 0.5 = 314.659 Step 3: Apply floor → floor(314.659) = 314 Step 4: Divide by 100 → 314 / 100 = 3.14
Result: 3.14
The result 3.14 is the value of π (pi) rounded to 2 decimal places. The third decimal digit was 1 (less than 5), so the second decimal place stayed at 4 rather than rounding up. This is the standard result you would expect when rounding π for everyday calculations such as finding the circumference or area of a circle.
Rounding reduces the number of digits in a number while keeping its value as close to the original as possible. It is one of the most frequently used operations in mathematics, science, finance, and everyday life.
| Concept | Definition | Example (N = 0.004567) | |---|---|---| | Decimal places | Digits after the decimal point | 3 dp → 0.005 | | Significant figures | All meaningful non-zero digits (and zeros between/after them) | 3 sf → 0.00457 |
Rounding adjusts the last kept digit based on the dropped digits (e.g., 3.17 → 3.2 to 1 dp), while truncating simply removes extra digits without adjustment (e.g., 3.17 → 3.1 to 1 dp). Truncation always moves the result toward zero.
Banker's rounding (round half to even) rounds a value ending in exactly .5 to the nearest even digit. For example, 0.5 → 0, 1.5 → 2, 2.5 → 2. It is used in financial systems and statistical software (like Python's built-in round()) to reduce systematic bias when averaging large datasets.
Follow the precision of your least precise measurement. If you measure a length as 3.4 cm (2 significant figures), your final answer should also be reported to 2 significant figures, even if intermediate steps use more digits.
Excel's ROUND function uses round half away from zero. However, floating-point binary representation can cause numbers like 2.5 to be stored as 2.4999999…, causing it to round down unexpectedly. Use ROUND(number, digits) explicitly rather than relying on cell formatting for critical calculations.
This calculator uses the 'round half up' rule (also called round half away from zero for positive numbers), which is the most common standard taught in schools and used in everyday calculations. If the digit being dropped is exactly 5, the preceding digit is rounded up.
Select 'Significant Figures' as the rounding mode, then enter the number of significant figures you need. For example, rounding 0.006789 to 3 significant figures gives 0.00679, because you count from the first non-zero digit.
Yes. Enter the negative number directly (e.g., −4.756). The calculator rounds the magnitude correctly. Under round half up, −4.5 rounds to −4 (toward zero), while round half away from zero gives −5. The calculator uses round half away from zero for consistency.
Rounding to 0 decimal places gives you the nearest whole integer. For example, 7.6 rounds to 8 and 3.2 rounds to 3.
Yes. Use a negative value for d to round to the left of the decimal point. For example, d = −1 rounds to the nearest 10 (e.g., 463 → 460), and d = −2 rounds to the nearest 100 (e.g., 463 → 500).
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