Calculator Form
Example Data Table
| Decimal | Fraction | Mixed Number | Percent |
|---|---|---|---|
| 0.125 | 1/8 | 1/8 | 12.5% |
| 0.5 | 1/2 | 1/2 | 50% |
| 1.75 | 7/4 | 1 3/4 | 175% |
| -2.4 | -12/5 | -2 2/5 | -240% |
| 3.0625 | 49/16 | 3 1/16 | 306.25% |
Formula Used
- Exact terminating decimal conversion: If a decimal has d decimal places, write it as an integer over 10d.
- Simplification: Divide the numerator and denominator by their greatest common divisor, often called the GCD.
- Mixed number form: Divide the numerator by the denominator. The quotient is the whole part, and the remainder stays over the denominator.
- Approximation mode: This version also finds a close fraction using a bounded continued fraction method and your chosen maximum denominator.
How to Use This Calculator
- Enter any standard decimal, such as 0.625, 2.75, or -3.125.
- Set a maximum denominator if you also want a simple approximate fraction.
- Choose the display precision for percentages and graph labels.
- Click Convert Decimal to show the result above the form.
- Review the exact fraction, mixed number, detailed table, and graph.
- Use the CSV or PDF buttons to export the current result.
Frequently Asked Questions
1. What does this calculator convert?
It converts a decimal value into its exact simplified fraction. It also shows a mixed number, a bounded approximation, a percentage equivalent, and step-by-step working for easier checking.
2. Does it simplify the fraction automatically?
Yes. The calculator reduces the fraction by dividing the numerator and denominator by their greatest common divisor, so the exact result is shown in lowest terms.
3. Can it handle negative decimals?
Yes. Negative signs are preserved through exact fraction, mixed number, percentage, and approximation outputs, so values like -2.4 are converted correctly.
4. Why is there an approximate fraction too?
Some decimals are easier to read with smaller denominators. The approximation gives a nearby fraction within your denominator limit, which helps when you want a cleaner estimate.
5. What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 1 3/4. It is another way to present an improper fraction like 7/4.
6. What decimals work best here?
This version is best for standard terminating decimals written in normal notation, such as 0.125 or 4.75. It is not designed for repeating decimal notation.
7. What do the CSV and PDF buttons export?
They export the current result shown on the page. The CSV file is useful for spreadsheets, while the PDF file is useful for reports, printouts, and sharing.
8. Why does the exact and approximate result sometimes match?
They match when the exact simplified denominator already falls within your chosen maximum denominator. In that case, the bounded approximation reaches the same value.