Quick Answer

3.456 rounded to 2 decimal places is 3.46 (half-up), 3.45 (floor), 3.46 (ceil), 3.45 (truncate), and 3.46 (half-even).

Number

Decimal Places

Common Examples

Input	Result
3.456, 2 places	3.46 (round), 3.45 (floor), 3.46 (ceil)
2.5, 0 places	3 (round), 2 (floor), 3 (ceil), 2 (half-even)
-3.456, 2 places	-3.46 (round), -3.46 (floor), -3.45 (ceil)
7.005, 2 places	7.01 (round)
100.9, 0 places	101 (round), 100 (floor/truncate)

How It Works

Rounding methods

Five rounding methods are commonly used in mathematics, programming, and finance:

Round (half-up) is the standard method taught in school. If the digit being dropped is 5 or greater, round the preceding digit up by one. Otherwise, leave it unchanged. 3.456 to 2 places becomes 3.46. This is what JavaScript’s Math.round() does for positive numbers.

Floor always rounds toward negative infinity. 3.7 floors to 3, and -3.2 floors to -4. This is JavaScript’s Math.floor().

Ceiling always rounds toward positive infinity. 3.2 ceils to 4, and -3.7 ceils to -3. This is JavaScript’s Math.ceil().

Truncate removes digits after the cutoff point, effectively rounding toward zero. 3.9 truncates to 3, and -3.9 truncates to -3. This is JavaScript’s Math.trunc().

Half-even (banker’s rounding) is used in financial calculations and IEEE 754 floating-point arithmetic. When the dropped digit is exactly 5 with no further digits, round to the nearest even number. So 2.5 rounds to 2, 3.5 rounds to 4, and 4.5 rounds to 4. This prevents systematic bias that accumulates when many values are rounded.

Comparison table for 2.5

Method	Result
Round (half-up)	3
Floor	2
Ceiling	3
Truncate	2
Half-even (banker’s)	2

Worked example

Round -7.3451 to 2 decimal places:

• Round (half-up): The third decimal is 5, so round up: -7.35
• Floor: Round toward negative infinity: -7.35
• Ceiling: Round toward positive infinity: -7.34
• Truncate: Drop digits toward zero: -7.34
• Half-even: Third decimal is 5 with more digits after, so round up: -7.35

Floor and half-up agree for negative numbers when the dropped portion exceeds 0.5. They differ at exactly 0.5 and for values just below it.

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Frequently Asked Questions

What rounding method does standard math use?

Standard mathematical rounding uses the half-up rule: if the digit being dropped is 5 or greater, round up. This is the method taught in most math courses and used by most general-purpose calculators.

What is banker's rounding?

Banker's rounding (half-even) rounds values ending in exactly 5 to the nearest even number. 2.5 becomes 2, 3.5 becomes 4. Financial institutions use this method because it eliminates the upward bias that accumulates when half-up rounding is applied to many transactions.

What is the difference between floor and truncate?

For positive numbers, floor and truncate give the same result. They differ for negative numbers: floor(-3.7) = -4 (toward negative infinity), while truncate(-3.7) = -3 (toward zero).

How many decimal places should I round to?

It depends on the context. Currency amounts typically use 2 decimal places. Scientific measurements use the number of significant figures appropriate for the instrument's precision. Statistical results often use 2-4 decimal places.

Does rounding introduce error?

Yes. Each rounding operation introduces a small error (the difference between the exact value and the rounded value). When many rounded values are summed, these errors can accumulate. Banker's rounding and higher-precision intermediate calculations help minimize cumulative rounding error.

Learn More

How to Round Numbers

Learn how to round numbers with step-by-step rules, worked examples for decimals and negatives, and a comparison of five rounding methods including banker's rounding.