What are the rounding rules?

Standard rounding (round half up): if the digit to be dropped is less than 5, round down (truncate). If 5 or greater, round up. Example: 3.45 rounded to 1 decimal = 3.5. 3.44 = 3.4. For 'round half to even' (banker's rounding): 2.5 rounds to 2 (already even); 3.5 rounds to 4 (nearest even). This reduces cumulative rounding bias in large datasets.

How do I round to the nearest 10, 100, or 1000?

To round to the nearest 10: look at the units digit. If < 5, round down; if ≥ 5, round up. 43 → 40; 47 → 50. To nearest 100: look at the tens digit. 342 → 300; 367 → 400. To nearest 1000: look at the hundreds digit. 3,499 → 3,000; 3,500 → 4,000.

Rounding Calculator

Enter a number and choose how many decimal places to round to and the rounding mode.

Rounding Modes Explained

Standard Rounding (half-up)

Round 2.5 → 3, round 2.4 → 2. The most common everyday rounding method.

Floor (round down)

Always rounds toward negative infinity: 2.9 → 2, −2.1 → −3.

Ceiling (round up)

Always rounds toward positive infinity: 2.1 → 3, −2.9 → −2.

Truncate

Drops extra digits without rounding: 2.9 → 2, −2.9 → −2.

Examples

Number	Standard	Floor	Ceiling	Truncate
3.456 (2 dp)	3.46	3.45	3.46	3.45
2.5 (0 dp)	3	2	3	2
-1.5 (0 dp)	-2	-2	-1	-1

Related Calculators

Rounding Rules and Methods

Standard rounding (round half up) is the most common: if the digit to be dropped is 5 or more, round up; otherwise round down. But there are several other methods used in different contexts. Banker's rounding (round half to even) is used in finance and Excel to reduce cumulative rounding error — 2.5 rounds to 2, and 3.5 rounds to 4. Round half down is occasionally used in probability. Truncation (always round toward zero) is common in programming languages like C and Java for integer division.

When rounding money, always use banker's rounding or always-round-up depending on your context — rounding errors compound over millions of transactions.

Rounding to Significant Figures vs Decimal Places

Decimal places fix how many digits appear after the decimal point. Significant figures fix how many total meaningful digits the number has. For example, 0.00423 rounded to 2 decimal places is 0.00 (useless!), but rounded to 2 significant figures is 0.0042 — because the leading zeros are not significant.

Number	2 decimal places	2 significant figures
3.14159	3.14	3.1
0.00723	0.01	0.0072
1,450.8	1,450.80	1,500

Rounding Rules and When to Apply Them

Standard rounding: if the digit to be dropped is 0–4, round down (keep the digit before it); if 5–9, round up (increase the digit before it by 1). 3.74 rounded to one decimal place → 3.7 (drop 4, round down). 3.75 rounded to one decimal place → 3.8 (5 rounds up). Rounding to a specific place: identify the target digit, look one position right, apply the rule, replace all digits to the right with zeros (or drop them for decimals).

Banker's rounding (round half to even): when the dropped digit is exactly 5 with nothing after it, round to the nearest even digit. 2.5 → 2, 3.5 → 4, 4.5 → 4, 5.5 → 6. This reduces systematic bias in large datasets. Floor rounds always down (floor(3.9)=3), ceiling always up (ceil(3.1)=4), and truncation removes digits without rounding (trunc(3.9)=3). Choose based on your application — financial calculations often use banker's rounding or truncation.

Rounding Method Comparison

Method	3.5	4.5	2.3	−2.7
Standard	4	5	2	−3
Banker's	4	4	2	−3
Floor	3	4	2	−3
Ceiling	4	5	3	−2
Truncate	3	4	2	−2