Calculator Inputs
Decimal Approximation Guide
Formula Used
Decimal-place rounding: rounded value = R(x × 10p) ÷ 10p.
Absolute error: |exact value − approximate value|.
Relative error: absolute error ÷ |exact value|.
Here, x is the exact value. The exponent p selects the rounding place. The function R follows your chosen rounding method.
How to Use
- Choose single or batch calculation mode.
- Enter a decimal, fraction, percentage, radical, constant, or expression.
- Select a rounding method and precision type.
- Set comparison options to test another approximation.
- Choose formatting and repeating-decimal controls.
- Calculate, copy, export CSV, or print as PDF.
Supported Input Examples
| Input type | Example | Meaning |
|---|---|---|
| Decimal | 12.34567 | A standard decimal number |
| Fraction | 7/12 | An exact rational value |
| Mixed number | 3 5/8 | Three and five eighths |
| Percentage | 18% | Equivalent to 0.18 |
| Radical | sqrt(2) | The square root of two |
| Constants | pi/3 | Pi divided by three |
| Scientific notation | 6.022e23 | A large exponential value |
| Expression | (5 + 7) / 9 | A supported arithmetic expression |
Decimal Places and Significant Figures
Decimal places count digits after the decimal point. Significant figures count meaningful digits from the first nonzero digit. Place-value mode rounds to tenths, whole numbers, tens, or larger units.
Frequently Asked Questions
1. What is a decimal approximation?
It is a nearby decimal representing an exact value. The precision controls the permitted detail. More digits usually reduce approximation error.
2. How does half-up rounding work?
Half-up checks the first discarded digit. Values of five or more increase the kept digit. Smaller values leave that digit unchanged.
3. What is banker’s rounding?
Banker’s rounding is also called half-even rounding. Exact halfway values move toward an even final digit. This reduces repeated rounding bias.
4. Is truncation the same as rounding?
No, truncation simply removes unwanted digits. It never checks the following digit. Rounding may increase the final retained digit.
5. Can the calculator detect recurring decimals?
Yes, exact fractions receive recurring-decimal analysis. The repeating sequence receives an overline. Very long cycles respect the selected digit limit.
6. What is absolute error?
Absolute error measures the direct numerical difference. It ignores the exact value’s scale. Smaller absolute error means a closer approximation.
7. What is relative error?
Relative error compares absolute error with value magnitude. It helps compare differently sized quantities. Relative error is undefined when the exact value equals zero.
8. Can I process several values together?
Yes, select batch mode first. Enter one value on each line. The same precision settings apply across all entries.
9. Which expressions are supported?
The parser supports arithmetic, parentheses, powers, and percentages. It also supports pi, e, and common functions. Unsupported text produces a clear validation message.