Number Rounding Calculator
Round numbers to decimal places, whole numbers, tens, hundreds, thousands, or significant figures.
Positive numbers, negative numbers, decimals, and scientific notation such as 1.2e5 are supported.
Rounding mode
Round to a fixed number of decimal places.
Rounded result
3.75
Round using the digit after the last decimal place kept
Original number
3.746
Rounding place
2 decimal places
Checked digit
6
Direction
Rounded up
Difference
0.004
Mode
Decimal places
3.746 rounded to 2 decimal places is 3.75.
Rounding Rules
Basic rounding
If the next digit is 5 or greater, round up.
Round down
If the next digit is 4 or less, round down.
Exact halfway values
Exactly halfway values round away from zero, so 4.5 rounds to 5 and -4.5 rounds to -5.
Decimal places
Round based on the digit immediately after the final decimal place kept.
Place values
Round to ones, tens, hundreds, thousands, and so on.
Significant figures
Count from the first non-zero digit.
Ceiling
Rounds up toward positive infinity.
Floor
Rounds down toward negative infinity.
Truncation
Cuts off digits without rounding.
Variable Explanations
Original number
The number entered by the user.
Rounded result
The number after applying the selected rounding rule.
Rounding place
The place value or decimal place being kept.
Checked digit
The digit immediately to the right of the rounding place.
Decimal places
Digits after the decimal point.
Significant figures
Meaningful digits in a number.
Difference
Rounded result minus original number.
How Rounding Works
Simpler value
Rounding replaces a number with a nearby simpler value.
Last digit kept
The rounding place is the final digit you keep.
Decision digit
The checked digit decides whether the kept digit changes.
Many targets
Numbers can be rounded to decimals, whole numbers, place values, or significant figures.
Practical use
Rounding helps with estimates, measurements, reporting, and readability.
Precision
Trailing zeros can show intended decimal precision.
Worked Examples
3.746 to 2 decimal places
Rounding place: hundredths
Checked digit: 6
Rule: 5 or more rounds up
Answer: 3.75
7.24 to 1 decimal place
Rounding place: tenths
Checked digit: 4
Rule: 4 or less rounds down
Answer: 7.2
842 to nearest hundred
Rounding place: hundreds
Checked digit: 4
Rule: 4 or less rounds down
Answer: 800
15,678 to nearest thousand
Rounding place: thousands
Checked digit: 6
Rule: 5 or more rounds up
Answer: 16,000
0.004567 to 2 significant figures
Rounding place: 2 significant figures
Checked digit: 6
Rule: 5 or more rounds up
Answer: 0.0046
99.95 to 1 decimal place
Rounding place: tenths
Checked digit: 5
Rule: 5 or more rounds up
Answer: 100.0
-4.5 to nearest whole
Rounding place: ones
Checked digit: 5
Rule: half away from zero
Answer: -5
Round vs floor vs ceiling
Rounding place: whole number
Checked digit: varies
Rule: methods differ by direction
Answer: 3.7 → 4, floor 3, ceiling 4
Rounding Decimals, Whole Numbers, and Significant Figures
Decimal places
Controls digits after the decimal. Example: 12.345 to 2 decimals = 12.35.
Whole-number place values
Controls tens, hundreds, thousands, and more. Example: 12,345 to nearest hundred = 12,300.
Significant figures
Controls meaningful digits. Example: 0.012345 to 3 significant figures = 0.0123.
Common Rounding Mistakes
Understanding Your Results
Rounded result
The simplified number after applying the selected rule.
Checked digit
The digit that decided whether to round up or down.
Direction
Whether the rounded value increased, decreased, or stayed equivalent.
Difference
How far the rounded value is from the original.
Significant figures
The number of meaningful digits retained.
Frequently Asked Questions
Choose the rounding place, look at the digit immediately to the right, then round up if that digit is 5 or greater and round down if it is 4 or less.
If the next digit is 5 or greater, round up. If it is 4 or less, keep the rounding digit the same.
This calculator rounds half away from zero, so 4.5 becomes 5 and -4.5 becomes -5. The digit kept always grows in magnitude at an exact midpoint.
Keep the selected number of digits after the decimal point, then use the next digit to decide whether to round up or down.
Look at the tenths digit. If it is 5 or greater, round to the next whole number. If it is 4 or less, keep the whole number.
Choose the place value to keep, then check the digit immediately to the right of that place.
Significant figures are meaningful digits counted from the first non-zero digit.
Decimal places count digits after the decimal point. Significant figures count meaningful digits from the first non-zero digit.
Round chooses the nearest value, floor rounds toward negative infinity, ceiling rounds toward positive infinity, and truncate cuts off digits without rounding.
Nearest-value rounding uses the same checked digit and rounds half away from zero, so -4.5 becomes -5. Floor and ceiling behave differently because they always move toward negative or positive infinity.
Usually round at the final step to avoid compounding rounding error.
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Related reading
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