Calculator Input
Use the form below to approximate any decimal value.
Plotly Graph
The chart compares the original value, the rounded result, and the nearby interval bounds.
Formula Used
Decimal Places
Multiply by 10d, round, then divide by 10d. This keeps exactly the requested number of decimal places.
Significant Figures
Shift the decimal using the order of magnitude, round the shifted number, then shift back. This preserves the requested number of meaningful digits.
Nearest Interval
Divide by the interval, round the quotient, then multiply back. This approximates a number to any custom step size.
Absolute Error: |approximation − original|
Relative Error: (absolute error ÷ |original|) × 100%
How to Use This Calculator
- Enter the decimal number you want to approximate.
- Choose decimal places, significant figures, or nearest interval.
- Pick a rounding mode that matches your rule or coursework.
- Fill in the active precision field.
- Press Calculate Approximation to show the result above the form.
- Review the graph, steps, error values, and export buttons.
Example Data Table
| Original Value | Method | Setting | Approximation | Absolute Error |
|---|---|---|---|---|
| 12.98765 | Decimal Places | 2 places | 12.99 | 0.00235 |
| 0.0047689 | Significant Figures | 3 figures | 0.00477 | 0.0000011 |
| 47.36 | Nearest Interval | 0.25 | 47.25 | 0.11 |
| -18.445 | Decimal Places | 1 place | -18.4 | 0.045 |
Frequently Asked Questions
1. What is decimal approximation?
Decimal approximation replaces a number with a nearby value that is easier to read, report, or calculate. The result is close, but not identical, so the calculator also shows the error.
2. What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point. Significant figures count meaningful digits starting from the first nonzero digit. Scientific work often prefers significant figures because they scale with the number size.
3. When should I use half-up rounding?
Half-up rounding is the common classroom rule. Values halfway between two options go away from zero. It is simple, familiar, and useful when you need standard school-style rounding results.
4. What is half-even rounding?
Half-even, often called bankers rounding, sends exact halfway cases to the nearest even digit. This reduces cumulative bias across many calculations, which is helpful in statistics, accounting, and repeated automated rounding.
5. Why can relative error be unavailable?
Relative error divides by the absolute value of the original number. When the original number is zero, division is impossible, so the calculator reports that relative error is not available.
6. Can I round to tenths, hundredths, or thousandths?
Yes. Choose the decimal-places method and enter 1 for tenths, 2 for hundredths, or 3 for thousandths. The calculator then scales, rounds, and restores the number automatically.
7. What does nearest interval mean?
Nearest interval rounds to any custom step size, such as 0.25, 0.5, 5, or 10. This is useful for pricing bands, measurement increments, packaging units, and engineering tolerances.
8. Why do some decimal values round unexpectedly on computers?
Computers store many decimals in binary form, so some values cannot be represented exactly. Tiny storage differences can affect borderline rounding cases, especially when many decimal digits are involved.