Rounding Calculator
Round numbers to any decimal place, integer, or significant figures.
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How Rounding Works
Rounding replaces a number with an approximation that has fewer significant digits. It reduces precision in exchange for simplicity, which is useful for financial reporting, scientific measurements, and everyday calculations.
Rounding to Decimal Places
To round to N decimal places: look at the (N+1)th decimal digit. If it is 5 or greater, round up (increase the Nth digit by 1). If it is less than 5, round down (keep the Nth digit unchanged). Example: round 3.14159 to 2 decimal places — the 3rd decimal is 1 (less than 5), so result is 3.14.
Rounding to Significant Figures
Significant figures are meaningful digits in a measurement. To round to N sig figs: identify the Nth significant digit, look at the next digit, and apply the same rule. Example: round 0.004567 to 3 sig figs — the 3rd sig fig is 6, next digit is 7 (≥5), so round up to 0.00457.
Rounding to the Nearest Integer or Power of 10
Round to the nearest whole number, ten, hundred, etc. by looking at the first digit being dropped. Example: 473 rounded to the nearest 10 — look at units digit (3 < 5), round down to 470. Rounded to nearest 100 — look at tens digit (7 ≥ 5), round up to 500.
Rounding rules vary in some contexts. "Round half up" (the standard) rounds 0.5 up. "Banker's rounding" (round half to even) rounds 0.5 to the nearest even number, reducing cumulative rounding error in financial calculations.
Worked Example: Multiple Rounding Modes
Take the number 7,483.5. Rounded to the nearest integer (round half up): 7,484. Rounded to the nearest ten: 7,480. Rounded to the nearest hundred: 7,500. Rounded to the nearest thousand: 7,000. This shows how the same number yields very different results depending on the precision level selected.
| Number | Nearest 10 | Nearest 100 | Nearest 1000 | 2 Decimal Places |
|---|---|---|---|---|
| 3.14159 | 0 | 0 | 0 | 3.14 |
| 473.68 | 470 | 500 | 0 | 473.68 |
| 9,850.255 | 9,850 | 9,900 | 10,000 | 9,850.26 |
Frequently Asked Questions
Standard rounding: if the digit after the rounding position is exactly 5 (with nothing or zeros after it), round up. 2.5 rounds to 3; 2.45 rounds to 2.5 when rounding to 1 decimal.
Look at the 4th decimal: 5 is 5 or greater, so round up the 3rd decimal from 1 to 2. Result: 3.142.
Truncating simply drops all digits after the chosen position without adjusting. 3.7 truncated to integer = 3. Rounding adjusts based on the dropped digit: 3.7 rounded to integer = 4.
Look at the tens digit. If 5 or more, round up the hundreds digit. If less than 5, keep the hundreds digit. Example: 1,450 → 1,500; 1,449 → 1,400.
Financial calculations involving many small rounding steps can accumulate errors. Tax calculations, interest computations, and currency conversions all require specific rounding rules to ensure consistency and compliance.
Banker's rounding (round half to even) rounds a number ending in exactly .5 to the nearest even digit. So 2.5 → 2, but 3.5 → 4. This method statistically eliminates cumulative bias when many values are rounded, and is the default in IEEE 754 floating-point arithmetic and many spreadsheet applications.
Standard rounding applies the same rule: look at the next digit. For −2.5 rounded to the nearest integer, "round half up" gives −2 (rounds toward positive infinity). "Round half away from zero" gives −3 (rounds away from zero regardless of sign). Different contexts use different conventions, so always confirm which method is required.