Scientific Notation Calculator

Rounding Calculator

Use this rounding calculator to round numbers to any decimal place or whole-number precision, choosing between standard half-up, banker's rounding, and truncation methods.

Round to any decimal placeHalf-up, banker's, and truncationStep-by-step deciding digit shown

Rounding Calculator

Round decimals, whole numbers, scientific notation values, and significant figures with clear steps.

Ready

Accepts decimals, negative numbers, and E notation such as 1.2345e-6.

Step by Step

Result Summary

Rounded value: 12345.68
Difference from original: 0.0011

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Rounding Calculator

A rounding calculator simplifies any number to a specified decimal place or integer precision and lets you choose the rounding method that fits your context. Standard half-up rounding is most common, but financial calculations often use banker's rounding to avoid systematic bias, while some engineering contexts call for truncation. This calculator supports all major methods and clearly shows which digit triggered the rounding decision.

What Is Rounding?

Rounding replaces a number with a nearby value that has fewer significant digits or fewer decimal places, while keeping the result as close as possible to the original. When rounding 3.746 to one decimal place, the second decimal (4) is less than 5, so the result stays at 3.7. When rounding 3.756 to one decimal place, the second decimal (5) is 5 or greater, so the tenths digit rounds up from 7 to 8, giving 3.8. Rounding is distinct from truncation, which simply drops digits without considering whether rounding up would give a closer result. Choosing the right method depends on whether you need symmetric rounding, least bias across large datasets, or speed.

How to Use the Rounding Calculator

Enter the number you want to round. The calculator accepts integers, decimals, and negative numbers. Choose the decimal place or whole-number level you want to round to—tenths, hundredths, thousandths, nearest ten, nearest hundred—and select the rounding method from the available options.

Click Calculate to see the rounded result and a step-by-step explanation identifying the deciding digit. The output shows which digit was examined, whether it triggered rounding up or down, and the final value. The panel also shows the truncated value at the same decimal level for comparison.

Worked Examples

Examples: 4.785 rounded to 2 decimal places = 4.79 (half-up); 2.5 rounded to nearest integer = 2 (banker's, since 2 is even) or 3 (half-up); 0.00456 rounded to 4 decimal places = 0.0046; and −7.35 rounded to 1 decimal place = −7.4 (half-up away from zero).

Common Rounding Problems

Frequent problems include rounding currency to the nearest cent, rounding measurement results to instrument precision, rounding intermediate results in multi-step calculations, and rounding statistical outputs such as means and standard deviations.

Rounding Rules and Method Comparison

These tables compare the main rounding methods and show the decimal-place rules that determine when and how each method acts.

Standard rounding (round half up)

In the half-up method, if the digit immediately after the last kept position is 5 or greater, round up. If it is less than 5, keep the last kept digit unchanged.

Value	Round to	Deciding digit	Result
3.745	2 decimal places	5 → round up	3.75
3.744	2 decimal places	4 → keep	3.74

Truncation (round toward zero)

Truncation drops all digits beyond the chosen position without considering the next digit. The result is always no larger in absolute value than the original.

Value	Round to	Truncated result	Half-up result
7.89	1 decimal place	7.8	7.9
−2.99	1 decimal place	−2.9	−3.0

Banker's rounding (round half to even)

Banker's rounding breaks ties by rounding to the nearest even digit when the deciding value is exactly 5 with nothing following. This reduces cumulative bias in large datasets.

Value	Round to integer	Deciding digit	Banker's result
2.5	integer	5 tie → 2 is even	2
3.5	integer	5 tie → 4 is even	4

Rounding to decimal places

The decimal place determines the last position to keep. Count from left to right after the decimal: tenths (1st), hundredths (2nd), thousandths (3rd), and so on.

Place name	Position	Example: 1.23456	Rounded result
Tenths	1st decimal	1.23456	1.2
Hundredths	2nd decimal	1.23456	1.23
Thousandths	3rd decimal	1.23456	1.235

Rounding negative numbers

Negative numbers can be rounded toward zero (truncation) or away from zero (symmetric half-up). Standard half-up rounds away from zero at tie cases.

Value	Method	Result	Direction
−2.5	Half-up (away from zero)	−3	Away from zero
−2.5	Truncation	−2	Toward zero
−2.5	Banker's rounding	−2	To even integer

Rounding whole numbers to nearest ten or hundred

Rounding integers to the nearest ten, hundred, or thousand follows the same rule: examine the digit in the next smaller place to decide whether to round up.

Value	Round to nearest	Deciding digit	Result
347	hundred	4 in tens place → keep	300
3750	thousand	7 in hundreds place → round up	4000

When to round: avoid premature rounding

Round only the final result of a calculation, not intermediate steps. Rounding too early introduces cumulative error that can shift the last significant digit of the final answer.

Scenario	Round when?	Correct approach	Risk of early rounding
Multi-step calculation	Final result only	Carry full precision through	Last digit may shift
Currency calculation	At payment point	Round to cent at end	Accumulates 0.01 errors

Process

Calculation Workflow

Enter value

Choose precision level

Apply rounding method

Show deciding digit and result

The calculator reads the input value and target precision, identifies the deciding digit just beyond the last kept position, applies the selected rounding method, and returns the rounded result with a clear explanation of the deciding step.

Input Formats

Supported Formats

Input style	Example
Decimal	3.74592
Negative number	−7.35
Large integer	34750
Small decimal	0.000456

Reference

Common Scientific Constants

Back to calculator

Constant name	Symbol	Notation value	Unit
Speed of light	c	2.99792458 x 10^8	m/s
Gravitational constant	G	6.67430 x 10^-11	N m^2/kg^2
Avogadro constant	NA	6.02214076 x 10^23	mol^-1

Questions

Calculator FAQ

What is rounding?

Rounding replaces a number with a nearby simpler value at a chosen precision level. The rounded value is the closest number to the original at that level. For example, 3.746 rounded to one decimal place is 3.7.

What is the half-up rounding rule?

In half-up rounding, if the digit after the last kept position is 5 or greater, increase the last kept digit by 1. If it is less than 5, leave it unchanged. This is the most common rounding method.

What is banker's rounding?

Banker's rounding resolves tie cases by rounding to the nearest even digit. For example, 2.5 rounds to 2 and 3.5 rounds to 4. This method minimizes cumulative upward bias when rounding many values.

What is the difference between rounding and truncating?

Rounding considers the digit after the last kept position to decide whether to go up or stay. Truncation simply drops digits beyond the chosen position without any check. Truncation always moves toward zero.

How do I round 3.745 to two decimal places?

Look at the third decimal digit, which is 5. Using half-up rounding, round the second decimal from 4 up to 5. The result is 3.75.

How do I round to the nearest tenth?

Examine the hundredths digit. If it is 5 or more, round the tenths digit up. If it is less than 5, keep it. For example, 6.48 rounds to 6.5, and 6.43 rounds to 6.4.

How do I round a negative number?

For standard half-up rounding, round negative numbers away from zero at the tie point. So −3.5 rounds to −4. For truncation, −3.5 becomes −3 because truncation moves toward zero.

When should I use banker's rounding?

Use banker's rounding when summing or averaging many values at the same precision, such as in financial accounting or statistical datasets. It prevents the systematic upward bias that half-up rounding accumulates.

What does rounding to the nearest hundred mean?

Rounding to the nearest hundred means keeping only the hundreds digit and above. Look at the tens digit: if it is 5 or more, round the hundreds digit up. For example, 350 rounds to 400 and 349 rounds to 300.

How is rounding different from significant figures?

Rounding to a decimal place targets a fixed digit position. Rounding to significant figures targets the first n meaningful digits starting from the first non-zero digit, which shifts with the number's magnitude.

What is truncation?

Truncation drops all digits after a chosen position without rounding. The absolute value of the result is always less than or equal to the original. For example, truncating 7.89 to 1 decimal place gives 7.8.

Why does early rounding cause errors?

Rounding intermediate results discards precision that may affect the final answer. Carry full precision through all steps and round only the final result to avoid cumulative rounding error.

Can I round to a negative decimal place?

Yes. Rounding to a negative decimal place means rounding to the nearest ten, hundred, or higher power of ten. For example, rounding to the −2 decimal place means rounding to the nearest hundred.

What is the floor function versus rounding?

The floor function always rounds down to the next lower integer toward negative infinity. Standard rounding rounds to the nearest integer. For example, floor(3.9) = 3, but rounded 3.9 = 4.

How do I round 0.00456 to four decimal places?

The fifth decimal digit is 6 (5 or greater), so round the fourth decimal up from 5 to 6. The result is 0.0046.