Calculator
Use exact conversion for terminating decimals, add repeating digits for recurring values, or apply approximation when you want a denominator cap.
Example data table
| Decimal input | Repeating digits | Mode | Fraction result | Mixed number |
|---|---|---|---|---|
| 0.75 | — | Auto exact conversion | 3/4 | 3/4 |
| 1.125 | — | Auto exact conversion | 9/8 | 1 1/8 |
| 2.3 | 3 | Repeating decimal formula | 7/3 | 2 1/3 |
| 0 | 142857 | Repeating decimal formula | 1/7 | 1/7 |
| 3.14159 | — | Approximate fraction | 355/113 | 3 16/113 |
Formula used
Terminating decimal: write the number over 10^n, where n is the number of decimal places. Then simplify by dividing both parts by the greatest common divisor.
Formula: fraction = decimal × 10^n / 10^n, then reduce.
Repeating decimal: if a digits do not repeat and b digits repeat, use (all digits − non-repeating digits) / (10^(a+b) − 10^a), then simplify.
Approximation mode: use continued fractions to find a close rational number within the chosen denominator limit and tolerance threshold.
How to use this calculator
- Enter the decimal value you want to convert.
- Add repeating digits only when the decimal repeats forever.
- Choose auto, repeating, or approximate conversion mode.
- Set a maximum denominator if you need simpler fractions.
- Adjust tolerance when using approximation for close rational matches.
- Enable solution steps to review the method used.
- Click Convert Decimal to place the result above the form.
- Download the result as CSV or PDF when needed.
Frequently asked questions
1. What decimal values can this calculator convert?
It converts terminating decimals exactly, repeating decimals with a repeating block, and non-terminating values through controlled approximation when a denominator limit is useful.
2. What should I enter for a repeating decimal?
Type the decimal part before repetition begins, then add only the recurring block. For 0.333..., enter 0 or 0. and repeat 3.
3. Why is simplification important?
Simplification reduces the fraction to lowest terms, making answers easier to compare, verify, teach, and use in later arithmetic operations.
4. When should I use approximation mode?
Use approximation when you want a cleaner fraction with a smaller denominator, or when the decimal comes from a rounded measurement or scientific notation.
5. What does the maximum denominator control?
It limits how large the denominator may become in approximation mode. Smaller limits usually produce simpler fractions, but the decimal match can become less exact.
6. Why does the mixed number look the same sometimes?
When the fraction is proper, the mixed-number form remains the same as the fraction. Mixed numbers mainly change improper fractions greater than one whole.
7. Can I export my result?
Yes. After calculating, use the CSV button for spreadsheet-friendly output or the PDF button for a neat report you can save or print.
8. How do I verify the fraction is correct?
Compare the decimal check value shown in the result box with your original decimal. Matching values confirm the converted fraction or the chosen approximation.