How to use the decimal to fraction converter
- Select Decimal to fraction or Fraction to decimal from the dropdown.
- Type your number into the active field. For repeating decimals, add an ellipsis like
0.333.... - Check or uncheck Show as mixed number to control the output format.
- The result updates instantly as you type.
How the decimal to fraction conversion works
To convert a terminating decimal to a fraction, count the digits after the decimal point. That count becomes the power of ten in the denominator. For example, 0.625 has three decimal places, so write it as 625 / 1000. Then simplify by dividing both parts by their greatest common divisor (GCD). The GCD of 625 and 1000 is 125, giving 5/8.
For a repeating decimal to fraction, use algebra. Take 0.333... where one digit repeats. Let x = 0.333... Multiply by 10 (since one digit repeats) to get 10x = 3.333... Subtract the original equation: 9x = 3, so x = 3/9 = 1/3. If there are non-repeating digits before the repeat, such as 0.1666..., let x = 0.1666... Multiply by 10 to shift past the non-repeating part (10x = 1.666...) and by 100 to shift past one full repeat (100x = 16.666...). Subtract: 90x = 15, so x = 15/90 = 1/6.
Common decimal to fraction reference table
This table lists frequently used conversions. Each fraction is fully simplified.
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.375 | 3/8 |
| 0.5 | 1/2 |
| 0.625 | 5/8 |
| 0.666... | 2/3 |
| 0.75 | 3/4 |
| 0.875 | 7/8 |
Converting a fraction to a decimal
The reverse operation, fraction to decimal, is straightforward division. Divide the numerator by the denominator. For a mixed number like 2 1/4, first convert it to an improper fraction: multiply the whole number by the denominator and add the numerator, giving 9/4. Then divide 9 by 4 to get 2.25.
Some fractions produce repeating decimals. For instance, 1/3 = 0.333... and 1/6 = 0.1666... The converter displays up to 12 significant digits and appends an ellipsis if the decimal repeats beyond that.
Proper, improper and mixed numbers
A proper fraction has a numerator smaller than its denominator, like 3/4. An improper fraction has a numerator equal to or larger than the denominator, like 7/4. A mixed number combines a whole number and a proper fraction, like 1 3/4.
When the "Show as mixed number" option is enabled, this decimal to fraction calculator outputs values greater than one or less than negative one as mixed numbers. So 2.625 becomes 2 5/8 instead of 21/8. Disable the checkbox to always see the improper fraction form.
Practical uses for these conversions
Carpenters, machinists and sewers often work with fractional inches (1/16, 1/8, 1/4) while digital calipers and measuring software display decimals. Converting between the two avoids rounding errors on the job site.
In cooking, recipes may list 0.75 cups of sugar, which is easier to measure as 3/4 cup. Students working through math homework also rely on quick conversions to check manual calculations. For more complex arithmetic with fractions, try the fraction calculator.
Edge cases and common mistakes
Negative numbers carry through normally: -0.75 simplifies to -3/4. Zero converts cleanly to 0/1. Very small decimals like 0.0001 become 1/10000.
A frequent mistake is treating a rounded decimal as exact. If a measurement reads 0.33, it equals 33/100, not 1/3. Only 0.333... (with the ellipsis indicating infinite repetition) equals 1/3. Always specify whether the trailing digits repeat or terminate to get the correct fraction.
Worked examples
Each result below was produced by the same code the tool runs, so you can check your own numbers against them.
| Example | Input | Result |
|---|---|---|
| 0.75 to fraction | Conversion direction: d2f; Decimal number: 0.75; Show as mixed number when possible: yes | Fraction: 3/4 |
| Repeating 0.333... | Conversion direction: d2f; Decimal number: 0.333...; Show as mixed number when possible: no | Fraction: 1/3 |
| Negative mixed: -2.625 | Conversion direction: d2f; Decimal number: -2.625; Show as mixed number when possible: yes | Mixed number: -2 5/8 |
| Fraction 3/8 to decimal | Conversion direction: f2d; Fraction: 3/8; Show as mixed number when possible: yes | Decimal: 0.375 |
| Mixed number 2 1/4 to decimal | Conversion direction: f2d; Fraction: 2 1/4; Show as mixed number when possible: yes | Decimal: 2.25 |
FAQ
How do I convert 0.875 to a fraction?
Write 0.875 as 875/1000 since there are three decimal places. The greatest common divisor of 875 and 1000 is 125. Dividing both by 125 gives 7/8.
Can this tool handle repeating decimals?
Yes. Type the repeating part followed by an ellipsis, such as 0.333... or 0.1666... The converter uses the algebraic method to find the exact fraction.
What is the difference between a mixed number and an improper fraction?
A mixed number like 1 3/4 includes a whole number and a proper fraction. An improper fraction like 7/4 expresses the same value with a numerator larger than the denominator.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For 3/8, compute 3 divided by 8 to get 0.375. Select the fraction to decimal mode in the tool above to do this automatically.
Is my data sent to a server?
No. All calculations run locally in your browser. Nothing you type is uploaded anywhere.
Why does 0.33 give 33/100 instead of 1/3?
Because 0.33 is a terminating decimal with exactly two decimal places. To get 1/3, you must indicate that the 3 repeats infinitely by typing 0.333... with an ellipsis.