Free · Rounding
Round to Thousandths with Nine Modes
Round a decimal to three places using the usual nearest rule or choose any of nine signed rounding modes, with a live example table.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
23.5481 rounds to23.548 under the default half-up rule.
Round the input to a multiple of0.001 using the selected decimal rounding rule.
Worked example
Enter these known values and leave the other values blank.
- Number
- 23.5481
- Result
- 23.548
- point6
- 0.6
- point727935
- 0.728
- point078
- 0.078
- twenty3Point5481
- 23.548
- sixPoint30054
- 6.301
- point0196
- 0.02
Assumptions and limitations
- The default half-up mode chooses the nearest thousandth; an exact tie goes away from zero. All nine captured modes remain available through the advanced toggle.
- Up and Down mean away from and toward zero. Ceil and Floor mean toward positive and negative infinity. Half up/down/even/ceil/floor choose the nearest value and use their named direction only at exact ties.
- The absolute number must not exceed9007199254740991.9999999999999999, matching the captured positive computational bound and extending it symmetrically to negative inputs. This is not a general mathematical rounding limit.
- All six example rows respond to the retained rounding-mode selector. Clearing a number leaves its result unknown; clearing the mode does not select a substitute. Tiny finite inputs use scientific formatting where needed, while outputs remain thousandth increments.
Common questions
How many decimal places is a thousandth?
Three. For example,1.23456 rounds to1.235 under the default half-up rule.
What does half even do at a tie?
It chooses the nearest thousandth whose last retained digit is even:1.2345→1.234 and1.2355→1.236.
Which number expressions can I enter?
Enter a finite decimal or scientific-notation number. Exact finite-decimal arithmetic such as 1/8 or 1−1 is supported. Repeating fractions such as 1/3, expressions that lose digits, functions, symbols and other bases are held; enter a decimal value instead. Computational proof limits are stated in the reference note. The ambiguous expression 0^0 is rejected.
References
Replace captured decimal string reconstruction and approximate floor splitting with source-bound Decimal rounding to exactly three decimal places, preserving all nine rounding modes and all six example rows. Exact native floor splitting keeps hidden whole/fraction parts consistent near integers. Preserve the captured maximum magnitude symmetrically for signed inputs and require a valid retained integer rounding mode. Scientific notation is limited to the existing tiny-value formatting fallback; the rounded result remains exactly at thousandth increments. Inputs accept finite decimal/scientific literals and provably exact finite-decimal arithmetic (+, −, ×, ÷ and bounded integer powers). Lossy, repeating, function, symbolic and other-base expressions are rejected: enter a decimal value instead. The ambiguous expression 0^0 is rejected. Proof work is bounded to 20000 characters/coefficient digits, 512 nodes, depth64, 10000 aligned decimal places or absolute integer exponent, and one million Euclidean digit-work units; these are computational limits, not physical domains. Only captured editable controls are accepted as manual/API inputs.