Conversion Result
Step-by-step solution
Equivalent fractions
Verification
Enter a Decimal
Calculation History
Recent results are stored in this browser only.
| Date | Input | Fraction | Mixed number | Accuracy | Actions |
|---|---|---|---|---|---|
| No calculations saved yet. | |||||
Formula Used
Terminating decimals
Fraction = integer digits ÷ 10n
Here, n is the number of digits after the decimal point. Divide the numerator and denominator by their greatest common divisor.
Repeating decimals
Fraction = (A − B) ÷ [10k(10r − 1)]
k counts non-repeating decimal digits. r counts repeating digits, while A and B represent joined digit blocks.
Approximation
Error = |entered decimal − fraction value|
A continued-fraction method finds a close result whose denominator does not exceed the selected limit.
How to Use This Calculator
- Select terminating, repeating, or mixed repeating decimal mode.
- Enter the decimal value or the non-repeating prefix.
- For recurring values, enter only the digits that repeat.
- Choose a preferred result format and display precision.
- Enable denominator limiting when you need a practical approximation.
- Select Calculate fraction to view the fraction, mixed number, percentage, proof, equivalents, and detailed steps.
Use the copy button for a text result. CSV exports calculation history, while PDF creates a printable conversion report.
Common Decimal and Fraction Examples
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.1 | 1/10 | 10% |
| 0.125 | 1/8 | 12.5% |
| 0.2 | 1/5 | 20% |
| 0.25 | 1/4 | 25% |
| 0.333… | 1/3 | 33.333…% |
| 0.375 | 3/8 | 37.5% |
| 0.5 | 1/2 | 50% |
| 0.625 | 5/8 | 62.5% |
| 0.75 | 3/4 | 75% |
| 1.5 | 3/2 = 1 1/2 | 150% |
Understanding Decimal to Fraction Conversion
A decimal and a fraction can describe the same quantity using different notation. Terminating decimals contain a finite number of digits after the decimal point, so conversion begins by removing that point and placing the resulting integer over a power of ten. The fraction then becomes simpler when both parts share a common factor.
For example, 0.625 has three decimal places, creating the initial fraction 625/1000. The greatest common divisor of 625 and 1000 is 125, so dividing both values by 125 produces 5/8. This reduced form is exact and returns 0.625 when divided.
Repeating decimals require a different algebraic pattern because their digits never end. The calculator separates any non-repeating prefix from the recurring block, builds two whole numbers, subtracts them, and uses a denominator containing nines and zeros. Therefore, 0.1 with 6 repeating becomes 15/90 and simplifies to 1/6.
A decimal greater than one may produce an improper fraction whose numerator exceeds its denominator. The same value can also appear as a mixed number, which combines a whole number with a proper fraction for easier reading. For instance, 2.75 equals 11/4 and also equals 2 3/4.
Approximation mode is useful when a long measured or calculated decimal does not need an enormous denominator. A continued-fraction process searches for a nearby ratio while respecting the maximum denominator selected by the user. The report clearly labels approximate results and shows both absolute and percentage error.
Precision settings control how many decimal places appear in verification and error values. Optional input rounding changes a terminating decimal before conversion, so it should be enabled only when rounded data is intentional. Exact recurring notation remains preferable when the repeating block is known.
Equivalent fractions multiply the numerator and denominator by the same nonzero number. They look different but preserve the same ratio, making them useful for comparison, teaching, and common-denominator work. Verification divides the final numerator by its denominator to confirm accuracy.
Negative decimals are handled by keeping the sign with the numerator while the denominator remains positive. Zero converts to 0/1, and whole numbers receive a denominator of one after simplification. Always check measurement precision before choosing an approximate fraction.
Frequently Asked Questions
How is a terminating decimal converted to a fraction?
Remove the decimal point, place the integer over a power of ten matching the decimal places, then reduce using the greatest common divisor.
Can the calculator convert repeating decimals exactly?
Yes. Enter the non-repeating prefix separately and place the recurring digits in the repeating-digits field.
What does mixed repeating decimal mean?
It has one or more non-repeating digits before a repeating block, such as 0.1(6) or 2.35(27).
Why does the calculator show an improper fraction?
Decimals above one naturally create fractions whose numerator may exceed the denominator. The mixed-number result shows the same value differently.
What is the maximum denominator option?
It restricts approximation results to a practical denominator, which is useful for measurements, recipes, dimensions, and quick estimates.
What is the difference between exact and approximate results?
An exact fraction equals the entered decimal representation. An approximate fraction is nearby and includes a calculated error value.
How are negative decimals handled?
The negative sign stays with the numerator. The denominator is always presented as a positive integer.
Why should a fraction be simplified?
Simplification produces the smallest whole-number numerator and denominator while preserving exactly the same mathematical value.
Does changing display precision alter the exact fraction?
No. Display precision changes visible decimal digits only, unless the separate input-rounding option is deliberately enabled.