What is the rounding rule for 5?

The standard rule is to round 5 up (e.g., 2.5 rounds to 3). Some scientific applications use "round half to even" (banker's rounding), where 2.5 rounds to 2 (nearest even) but 3.5 rounds to 4. This reduces bias when summing many .5 cases.

What is the difference between rounding and truncating?

Rounding adjusts to the nearest value (3.7 rounds to 4, 3.2 to 3). Truncating simply cuts off extra digits (3.7 truncates to 3, 3.2 to 3). Rounding is more accurate; truncating always moves toward zero. Different behaviors for negatives.

When should I round numbers?

Round when reporting final results, not during intermediate calculations. Rounding too early introduces accumulation errors. Keep extra precision during calculations and round only the final answer for display or reporting.

What's banker's rounding?

Round half to even: 0.5 → 0, 1.5 → 2, 2.5 → 2, 3.5 → 4. Reduces statistical bias when summing many .5 cases (half round up, half round down). Used in IEEE 754 floating-point and most scientific computing. Different from standard "round half up".

How do I round to nearest 10, 100, etc.?

Same idea, just different precision. For nearest 10: look at units digit. 47 → 50, 42 → 40. For nearest 100: look at tens digit. 463 → 500, 432 → 400. Standard half-up rule applies for the boundary case.

What's the difference between floor and truncate?

For positive numbers: same result. For negatives: differ. Floor(-3.7) = -4 (toward negative infinity). Truncate(-3.7) = -3 (toward zero). Floor always more negative; truncate always toward zero. Programming languages may use either.

Why does 0.1 + 0.2 not equal 0.3 in computers?

Binary floating-point can't represent 0.1 or 0.2 exactly (they're repeating decimals in binary). Addition gives ~0.30000000000000004. Most languages' default print suppresses this. For exact decimal arithmetic, use special decimal types (Python's Decimal, Java's BigDecimal).

How do I round to significant figures?

Count significant digits from leftmost non-zero. Round at the desired position. For 3.14159 to 3 sig figs: digits 3, 1, 4. Look at next (1), round down: 3.14. For 12,345 to 2 sig figs: 12,000. For 0.00345 to 2 sig figs: 0.0035.

Rounding Calculator

Round any number to a specific decimal place, number of significant figures, or to the nearest integer, ten, hundred, or thousand. See the rounded result and the rounding direction.

Rounding is the process of approximating a number to fewer digits, sacrificing precision for simplicity. We round prices ($19.99 → $20), measurements (3.14159 → 3.14), statistics (52.347% → 52%), and report only meaningful digits. Rounding is essential for clear communication, sensible measurement reporting, and reducing computational complexity.

The standard rule: look at the digit just past where you want to round. If 5 or more, round up; if less than 5, round down. So 3.14159 rounded to 2 decimal places: look at third decimal (1, less than 5), round down to 3.14. Rounded to 3 decimal places: look at fourth (5, exactly 5), round up to 3.142.

Several rounding conventions exist for "exactly 5": - **Half up** (standard): always round up. 2.5 → 3, -2.5 → -2 (or -3). - **Half down**: always round down. 2.5 → 2. - **Half to even** (banker's): round to even number. 2.5 → 2, 3.5 → 4. - **Half away from zero**: away from zero. 2.5 → 3, -2.5 → -3.

"Half to even" reduces statistical bias when summing many rounded values; used in financial calculations and IEEE 754 floating-point standards.

Rounding directions: - **Round (default)**: nearest value. - **Round up (ceiling)**: always toward positive infinity. - **Round down (floor)**: always toward negative infinity. - **Truncate**: drop digits, toward zero.

Common applications: financial reporting, scientific measurement, statistical analysis, data presentation, currency rounding, and any situation requiring concise number representation.

Inputs

Number to Round

Round To

Results

Rounded

3.14

Rounded Up

3.15

Rounded Down

3.14

Direction

Rounded down

Rounding Details

Method	Result
Original Number	3.14159265
Rounding To	2 decimal places
Rounded (standard)	3.14
Rounded Up (ceiling)	3.15
Rounded Down (floor)	3.14
Truncated	3.14
Direction	Rounded down
Difference	0.00159265

Last updated: May 29, 2026

Formula

**Standard rounding (half up):** To round x to n decimal places: 1. Multiply x by 10^n. 2. Add 0.5. 3. Truncate (floor). 4. Divide by 10^n. Or use built-in rounding functions in calculators/programming. **Worked example: Round 3.14159 to 2 decimal places:** 3.14159 × 100 = 314.159. 314.159 + 0.5 = 314.659. Floor = 314. 314 / 100 = 3.14. Result: 3.14. **For rounding to 3 decimal places:** 3.14159 × 1000 = 3141.59. 3141.59 + 0.5 = 3142.09. Floor = 3142. 3142 / 1000 = 3.142. Result: 3.142. **Different rounding rules:** | Number | Half up | Half to even (banker's) | Half down | |---|---|---|---| | 0.5 | 1 | 0 | 0 | | 1.5 | 2 | 2 | 1 | | 2.5 | 3 | 2 | 2 | | 3.5 | 4 | 4 | 3 | | 4.5 | 5 | 4 | 4 | | 5.5 | 6 | 6 | 5 | Banker's rounding distributes 0.5 cases 50/50. **Rounding negative numbers:** For -2.5: - Half up: -2 (toward zero gives -2, away gives -3; convention varies). - Half away from zero: -3. - Half to even: -2. - Half down: -3. Various languages handle differently — check documentation. **Rounding to powers of 10:** To nearest 10: round 47 → 50, 142 → 140. To nearest 100: round 463 → 500, 1234 → 1200. To nearest 1000: round 6789 → 7000. Same idea: look at digit one place smaller than rounding place. **Round vs floor vs ceiling vs truncate:** For 3.7: - Round: 4 (nearest). - Floor: 3 (down). - Ceiling: 4 (up). - Truncate: 3 (toward zero). For -3.7: - Round: -4 (nearest, sign depends on convention). - Floor: -4 (down, more negative). - Ceiling: -3 (up, less negative). - Truncate: -3 (toward zero). **Floor vs truncate for negatives:** - **Floor(-3.7) = -4** (toward negative infinity). - **Truncate(-3.7) = -3** (toward zero). Different for negatives! Same for positives. **Significant figures rounding:** For 3.14159 to 3 sig figs: First 3 sig figs: 3, 1, 4. Round to 3 sig figs: 3.14. For 12,345 to 2 sig figs: First 2 sig figs: 1, 2. Round: 12,000. For 0.00345 to 2 sig figs: First 2 sig figs: 3, 4. Round: 0.0035 (look at next digit, which is 5, so round up). **Banker's rounding (IEEE 754):** Round half to even: - 0.5 → 0 (even). - 1.5 → 2 (even). - 2.5 → 2 (even). - 3.5 → 4 (even). Used in finance and floating-point arithmetic to reduce bias. If you have many .5 cases, equal split between rounding up and down. Standard in JavaScript Math.round? No, that's half away from zero. Python's round()? Yes, banker's rounding. **Common applications:** - **Financial**: rounding cents in calculations. - **Currency conversion**: typically 2 decimal places. - **Scientific reporting**: appropriate sig figs. - **Statistics**: clean numbers for presentation. - **Engineering**: tolerance and precision specifications. - **Manufacturing**: dimensional accuracy. - **Data visualization**: avoid spurious precision. - **Programming**: display formatting. **Rounding errors and accumulation:** Rounding too aggressively early can accumulate errors: - 1/3 + 1/3 + 1/3 = 1 (exact). - 0.33 + 0.33 + 0.33 = 0.99 (rounded early). - 0.333 + 0.333 + 0.333 = 0.999. For accurate sums of fractions: keep precision until final. **Significant figures:** Number of meaningful digits. Rounding to sig figs preserves precision better than to decimals for very small or large numbers. 3,456,000 to 3 sig figs: 3,460,000. 0.000345 to 3 sig figs: 0.000345. 0.0034567 to 3 sig figs: 0.00346. **Programming examples:** | Language | Round to int | Round to n decimals | |---|---|---| | Python | round(x) | round(x, n) | | JavaScript | Math.round(x) | manual or toFixed(n) | | Java | Math.round(x) | BigDecimal.setScale | | C++ | std::round(x) | manual | | Excel | =ROUND(A1, 0) | =ROUND(A1, n) | | R | round(x, n) | | | MATLAB | round(x, n) | | Each language has slight differences in rounding rules (especially for .5 cases). **Practical examples:** **Restaurant tip rounding:** Bill $47.83. 18% tip: $8.6094. Round: $8.61. **Sales tax:** $25.50 × 8.25% = $2.10375. Round: $2.10. **Salary calculation:** Hourly $24.75 × 40 hrs/week × 52 weeks = $51,480 exactly. No rounding needed. But: $24.75 × 80.5 hrs = $1,992.375 → round to cent: $1,992.38 (half up) or $1,992.37 (half to even). **Population statistics:** Median income $58,723.45 — typically reported as $58,723 (integer dollars) or rounded to thousands: $59,000. **Currency formats:** USD: 2 decimal places typical ($10.50). JPY: 0 decimal places (¥100,000). EUR: 2 decimal places (€15.99). Cryptocurrencies: often many decimal places (0.00000001 BTC = 1 satoshi). **Rounding standards:** - **ASTM E29**: rounding standard for engineering. - **IEEE 754**: floating-point arithmetic (banker's rounding). - **Financial GAAP**: typically half up for cents. - **Scientific**: half to even (banker's) common. **Software:** - **Excel**: ROUND, ROUNDUP, ROUNDDOWN, MROUND, CEILING, FLOOR. - **Python**: round (banker's), math.floor, math.ceil, math.trunc. - **JavaScript**: Math.round, Math.ceil, Math.floor, Math.trunc. - **Most spreadsheets**: similar function suite. **Pitfalls:** - **Rounding before final step**: accumulates errors. - **Sign on negatives**: round half toward zero or away from zero? - **Banker's vs standard**: 2.5 → 2 (banker's) vs 3 (standard). - **Floor vs truncate for negatives**: -3.7 → -4 (floor) vs -3 (truncate). - **Floating-point precision**: 0.1 + 0.2 ≠ 0.3 exactly. - **Mixing currency conventions**: USD vs JPY rounding.

How to use this calculator

Enter the number to round.
Select rounding precision: decimals, integer, tens, etc.
Calculator returns rounded value.
Standard rule: 5 and above rounds up; below 5 rounds down.
For very precise work: use banker's rounding (round half to even).
For significant figures: see sig-figs calculator.

Worked examples

Currency rounding

**Scenario:** $123.456 should display as currency. Round to 2 decimal places. **Calculation:** Look at third decimal: 6 (≥ 5), round up. 123.456 → 123.46. **Result:** $123.46. Standard for US currency. For pricing displays, sometimes round to .99 or .95 for psychological pricing.

Pi rounding

**Scenario:** Round π = 3.14159265 to 4 decimal places. **Calculation:** Fifth decimal is 9 (≥ 5), round up. 3.14159 → 3.1416. **Result:** π ≈ 3.1416 (4 decimal places). For 2 decimal: π ≈ 3.14. For 6: π ≈ 3.141593. More precision than ~7 places rarely needed in practice.

Population statistics

**Scenario:** City population: 458,723. Round to nearest 10,000 for media reporting. **Calculation:** Look at thousands digit: 8 (≥ 5), round up. 458,723 → 460,000. **Result:** "460,000 residents" — easier to remember than exact figure. Common for journalism, presentations. For census reporting, exact numbers preserved.

When to use this calculator

**Use rounding for:**

- **Currency display**: 2 decimal places typically. - **Measurement reporting**: appropriate precision. - **Statistical presentation**: avoid spurious precision. - **Mental math**: simpler numbers. - **Data visualization**: clean numbers on charts. - **Engineering specs**: tolerance management. - **Programming**: display formatting. - **Final answers**: clean up calculations.

**Don't round during intermediate calculations:**

Rounding errors accumulate. Keep full precision until final result.

Example: ((1/3) × 3) − 1. Exact: 0. Rounded to 2 dp: ((0.33 × 3) − 1) = 0.99 − 1 = -0.01.

Small error becomes significant in summing many rounded values.

**Rounding conventions:**

- **Half up** (most common): 2.5 → 3. - **Half to even** (banker's, IEEE 754): 2.5 → 2, 3.5 → 4. - **Half down**: 2.5 → 2. - **Half away from zero**: 2.5 → 3, -2.5 → -3.

Default in most programming languages varies. Python uses banker's; JavaScript Math.round uses half away from zero (but inconsistently with negatives).

**Significant figures vs decimal places:**

- **Decimal places**: count after decimal point. 12.34 has 2 decimal places. - **Sig figs**: count all meaningful digits. 12.34 has 4 sig figs. 12,300 has 3 sig figs (if zero is just placeholder).

For scientific work, sig figs often more appropriate than decimal places.

**Common applications:**

- **Currency**: dollars and cents. - **Tips**: rounded to whole or quarter dollars. - **Discounts**: 25% off, rounded prices. - **Tax calculation**: rounding per item or per total. - **Engineering tolerances**: ±0.01 inch. - **Architecture**: dimensions to nearest 1/16 inch. - **Scientific data**: appropriate sig figs. - **Statistics**: median income, average age.

**Floor/Ceiling functions:**

- **Floor(x)**: largest integer ≤ x. Floor(3.7) = 3, Floor(-3.7) = -4. - **Ceiling(x)**: smallest integer ≥ x. Ceiling(3.2) = 4, Ceiling(-3.2) = -3.

Used in: - **Page count**: 11 items / 4 per page → ceil(11/4) = 3 pages. - **Time blocks**: 35 minutes → ceil(35/15) × 15 = 45 min slot. - **Inventory**: floor(quantity / case) for full cases needed.

**Truncation:**

Drop all digits past a point. For 3.7891 truncated to 2 decimal places: 3.78 (not 3.79). Always toward zero.

Different from rounding! Useful for: - Display formatting (don't round up). - Programming integer division. - Financial calculations (don't inflate fractional cents).

**Programming:**

- **Python**: round(x, n) uses banker's rounding. - **JavaScript**: Math.round inconsistent; better libraries. - **Java**: Math.round half-up; BigDecimal for precision. - **C#**: Math.Round(x, n, MidpointRounding) lets you choose. - **Excel**: ROUND uses half-up; ROUNDUP, ROUNDDOWN explicit.

**Software:**

- **Calculators**: built-in round function. - **Programming**: language-specific functions (check rounding mode). - **Spreadsheets**: ROUND, MROUND, FLOOR, CEILING. - **Financial software**: explicit rounding modes for accuracy.

**Educational notes:**

Rounding rules vary by curriculum: - US elementary: round half up. - Scientific notation: round to specific sig figs. - IEEE 754: round to even.

Be aware of which convention your context uses.

**Pitfalls:**

- **Rounding too early**: accumulates errors. - **Inconsistent rules**: half up vs half to even. - **Negative numbers**: rounding direction matters. - **Floor vs truncate**: differ for negatives. - **Floating-point**: 0.1 + 0.2 ≠ 0.3 in most languages. - **Currency edge cases**: 0.5 cents — varies by jurisdiction. - **Sig figs vs decimals**: confusion in scientific contexts. - **Rounding then comparing**: comparison results can be misleading.

**Special rounding rules:**

**Time rounding** (in business): - Round to nearest 6 minutes (1/10 hour) for payroll. - Round to nearest 15 minutes (1/4 hour) for invoicing.

**Currency rounding:** - USD: 2 decimal places (cents). - JPY: 0 decimals. - Cryptocurrency: variable, often 6-8 decimals.

**Scientific:** - Round to appropriate sig figs (based on measurement precision). - Last digit shouldn't be more precise than input.

**Pitfalls (continued):**

- **Banker's on currency**: some financial regulations require half-up. - **Inconsistent rules across team**: clarify which is being used. - **Rounding for display vs calculation**: keep raw values; round only for display. - **Negative zero issues**: -0.05 → 0 or -0.1 depending on rule. - **Cumulative rounding**: better to round once at the end than at each step.

Common mistakes to avoid

Rounding intermediate calculations instead of final result.
Inconsistent rounding rules across calculations.
Confusing floor (toward negative infinity) with truncate (toward zero) for negatives.
Using standard rounding (half up) in financial systems requiring banker's rounding.
Mixing rounding to decimal places vs significant figures.
Forgetting that 0.5 cases vary by rounding rule.
Floating-point precision issues (0.1 + 0.2 ≠ 0.3).
For currency: not handling fractional cents per local convention.

Frequently Asked Questions

Sources & further reading

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