Rounding Calculator

The Rounding Calculator changes a number to a requested place value or number of significant figures. The chosen rule matters at a halfway value: standard classroom rounding, round-half-even, floor, ceiling, and truncation can produce different results.

Decimal places versus significant figures

For ordinary nearest-place rounding, inspect the digit immediately to the right of the retained place. Digits 5–9 increase the retained digit; 0–4 leave it unchanged. Remove or replace the following digits according to the position.

Keep digits through the requested place and inspect the next digit; values 5 or greater conventionally increase the retained digit by one.

Enter the values in their mathematical roles

Enter the original value, choose decimal places or significant figures, and select a rounding mode when available. Preserve the unrounded value for later calculations. Negative numbers require special attention because floor moves toward negative infinity while truncation moves toward zero.

The governing relationship

Keep digits through the requested place and inspect the next digit; values 5 or greater conventionally increase the retained digit by one.

A compact example

Rounding 12.746 to two decimal places gives 12.75.

Valid inputs and boundary cases

Leading zeros are not significant, while zeros between nonzero digits are. Trailing zeros after a decimal can communicate precision. Scientific notation makes significant-figure intent clearer for very large or small values.

Read the answer in context

A calculator may use a specified tie-breaking rule; do not round intermediate values unnecessarily.

An independent check

Locate the retained digit and the next discarded digit on a place-value chart. Check whether the rounded result lies at the correct interval endpoint or midpoint, and confirm its precision matches the instruction.

Errors that change the answer

• Confusing decimal places with significant figures
• Rounding at every intermediate step
• Dropping meaningful trailing zeros
• Treating floor and truncation as identical for negatives
• Applying a halfway rule without naming it

Continue with a related calculator

Continue with the Prime Factorization Calculator or Long Division Calculator. For everyday arithmetic and order-of-operations checks, use the Basic Calculator.

What this numerical result cannot decide

Rounding reduces detail and can introduce cumulative error. Legal, financial, laboratory, and statistical standards may prescribe a particular rule; use that rule rather than assuming “round up at five” always applies.

A second way to understand the method

Rounding 0.004876 to three decimal places gives 0.005, while three significant figures gives 0.00488. Decimal places count positions after the decimal point; significant figures begin at the first nonzero digit and describe the precision of the value.

Carry propagation can change several digits

Rounding 9.996 to two decimal places inspects the third decimal, 6. The hundredths digit increases, carrying through the two 9s and producing 10.00. The trailing zeros communicate the requested decimal precision; writing only 10 may lose that information even though the numerical value is equal.

Rounding and truncation answer different instructions

Truncating 4.789 to two decimal places gives 4.78 because later digits are discarded. Ordinary nearest rounding gives 4.79. For −4.789, truncation gives −4.78, floor to two places gives −4.79, and ceiling gives −4.78. Name the method whenever the distinction affects the outcome.

Negative-place rounding

Places to the left of the decimal can also be selected. Rounding 48,650 to the nearest hundred inspects the tens digit and gives 48,700 under ordinary half-up rules. Rounding to the nearest thousand inspects the hundreds digit and gives 49,000. Confirm both the target place and the halfway convention.

Rounding Calculator FAQ

What is 12.49 to the nearest whole number?

It rounds to 12 because the tenths digit is 4.

Does 2.5 always round to 3?

Not under every rule; half-even rounding sends 2.5 to 2.

Should I round intermediate answers?

Usually keep extra digits and round the final result unless a standard says otherwise.

For additional worked mathematics, see the free OpenStax Prealgebra 2e reference.