Calculation history
Completed single calculations appear here in this browser.
Formula used
Decimal-place rounding: multiply by 10p, round to an integer using the selected method, then divide by 10p.
Custom increment: rounded value = round(number ÷ increment) × increment.
Absolute error: |rounded value − original value|.
How to use this calculator
- Select place value, decimal places, significant figures, or a custom increment.
- Choose the rounding method that matches your requirement.
- Enter one decimal or paste a batch of values.
- Choose whether trailing zeros should remain visible.
- Calculate, review the detailed steps, and inspect the error and boundaries.
- Copy results, download batch data as CSV, or print the page as a PDF.
Example calculations
| Number | Target | Method | Result | Reason |
|---|---|---|---|---|
| 47.3862 | Hundredth | Half-up | 47.39 | The deciding digit is 6, so the hundredths digit increases. |
| 12.345 | Hundredth | Half-even | 12.34 | The value is exactly halfway, and 4 is already even. |
| -8.21 | Whole number | Floor | -9 | Floor moves toward negative infinity. |
| 0.004987 | Three significant figures | Half-up | 0.00499 | The first significant digits are 4, 9, and 8; the next digit is 7. |
| 7.38 | Increment 0.25 | Half-up | 7.50 | 7.38 is nearer to 7.50 than 7.25. |
Understanding decimal rounding
Decimal rounding replaces a detailed value with a nearby simpler value. The selected place controls the unit that remains visible. Digits to the right determine whether that retained unit changes.
Standard half-up rounding increases the retained digit when the discarded portion reaches one-half. Other methods treat exact halves or negative numbers differently. Selecting the correct method prevents inconsistent financial and statistical results.
Significant figures measure meaningful digits rather than fixed decimal positions. Small values may require many decimal places to preserve three significant figures. Large values may round at tens, hundreds, or thousands.
Custom increments are useful for pricing, cash denominations, measurements, and scheduling. A value can be rounded to the nearest five cents, quarter unit, five, or hundred. The calculator shows the quotient and multiplication steps.
Rounding creates an error because the displayed result differs from the original. Absolute error shows the size of that difference. Percentage error compares it with the original magnitude.
Trailing zeros communicate precision in many scientific contexts. For example, 2.50 usually suggests hundredth-level precision, while 2.5 suggests tenth-level precision. The preservation option controls that visual distinction.
Frequently asked questions
What is the basic decimal rounding rule?
Keep the selected digit, inspect the next digit, and increase the retained digit when the chosen method requires it.
What is banker’s rounding?
Half-even rounding sends exact halfway values to the result with an even retained digit, reducing repeated upward bias.
How are negative numbers rounded?
Nearest methods compare magnitude, while ceiling and floor follow positive or negative infinity. Toward-zero and away-from-zero methods explicitly control direction.
Is truncation the same as rounding?
No. Truncation simply removes digits. Nearest-value rounding may increase the retained digit based on the discarded portion.
How do significant figures differ from decimal places?
Decimal places count digits after the decimal point. Significant figures count meaningful digits beginning with the first nonzero digit.
Why preserve trailing zeros?
Trailing zeros can show intended precision. A result of 4.50 communicates a different measurement resolution than 4.5.
What are rounding boundaries?
They are the lower and upper values that define the interval normally associated with a rounded result under nearest-value methods.
Can I round several values at once?
Yes. Paste numbers separated by commas, semicolons, or new lines, then download the completed table as a CSV file.
Why can custom increments show tiny precision differences?
PHP floating-point arithmetic represents many decimal fractions approximately. The calculator formats the output to match the increment’s practical precision.