Decimal to Fraction Calculator
Type a decimal to get it as a simplified fraction and a mixed number, with every step shown. Works with repeating decimals like 0.(3).
Repeating digits go in brackets:
3/4
Mixed number:
Steps
- 0.75 has 2 digits after the decimal point, so write it over 10^2 = 100: 75/100.
- The greatest common divisor of 75 and 100 is 25. Divide both: 75 ÷ 25 = 3, 100 ÷ 25 = 4.
How to convert a decimal to a fraction
- Count the decimal places. 0.625 has three digits after the point.
- Write the number over a power of ten. Three places means 1000: 0.625 = 625/1000.
- Simplify. The greatest common divisor of 625 and 1000 is 125, so 625/1000 = 5/8.
- Make a mixed number if needed. For 2.625 the same steps give 21/8, which is 2 5/8.
Worked examples
- .125 → 125/1000 → 1/8
- 0.01 → 1/100
- 10.(6) (10.666…) → 32/3 = 10 2/3
- 10.6666666667 (typed exactly) → 106666666667/10000000000
Working in inches? Use the decimal to fraction inches calculator to round to the nearest 1/16, 1/32 or 1/64 inch.
Repeating decimals
A repeating decimal never ends, so it cannot be written over a power of ten. Instead, shift it and subtract. For 0.1(6) = 0.1666…: 100x = 16.(6) and 10x = 1.(6). Subtracting gives 90x = 15, so x = 15/90 = 1/6.
Common decimals as fractions
| Decimal | Fraction | Mixed |
|---|---|---|
0.1 | 1/10 | — |
0.111… = 0.(1) | 1/9 | — |
0.125 | 1/8 | — |
0.1666… = 0.1(6) | 1/6 | — |
0.2 | 1/5 | — |
0.222… = 0.(2) | 2/9 | — |
0.25 | 1/4 | — |
0.333… = 0.(3) | 1/3 | — |
0.375 | 3/8 | — |
0.4 | 2/5 | — |
0.5 | 1/2 | — |
0.6 | 3/5 | — |
0.625 | 5/8 | — |
0.666… = 0.(6) | 2/3 | — |
0.7 | 7/10 | — |
0.75 | 3/4 | — |
0.8 | 4/5 | — |
0.8333… = 0.8(3) | 5/6 | — |
0.875 | 7/8 | — |
0.9 | 9/10 | — |
0.0625 | 1/16 | — |
0.08333… = 0.08(3) | 1/12 | — |
0.142857142857… = 0.(142857) | 1/7 | — |
0.090909… = 0.(09) | 1/11 | — |
1.5 | 3/2 | 1 1/2 |
2.25 | 9/4 | 2 1/4 |
Brackets mark repeating digits. Every value in this table is generated by the same calculator code.
Frequently asked questions
Do you turn a decimal into a fraction?
Yes. Write the decimal over a power of ten and simplify. For example .125 = 125/1000, and dividing both by 125 gives 1/8. A repeating decimal such as 0.(3) also has an exact fraction (1/3).
What is .125 as a fraction?
.125 = 125/1000 = 1/8.
What is 0.01 as a fraction?
0.01 = 1/100 (one hundredth). It is already in lowest terms.
What is 10.6666666667 as a fraction?
If the 6 repeats forever, enter 10.(6): it equals 32/3, or 10 2/3 as a mixed number. The rounded decimal 10.6666666667 typed exactly is 106666666667/10000000000, because a finite decimal is never exactly 2/3.
How do you convert a decimal to a fraction?
Write the digits after the decimal point over 1 followed by as many zeros as there are digits, then divide the top and bottom by their greatest common divisor. For example, 0.75 = 75/100, and dividing both by 25 gives 3/4.
How do I enter a repeating decimal?
Put the repeating digits in brackets. 0.333… is 0.(3), 0.1666… is 0.1(6) and 0.142857142857… is 0.(142857). Only the digits inside the brackets repeat.
How do you convert a repeating decimal to a fraction?
Multiply the number by a power of 10 that moves one full repeating block to the left of the decimal point, subtract the original number so the repeating part cancels, and solve. For x = 0.(3): 10x − x = 3.(3) − 0.(3) = 3, so 9x = 3 and x = 1/3.
Is 0.999… really equal to 1?
Yes. Using the same method, 10x − x = 9.(9) − 0.(9) = 9, so 9x = 9 and x = 1. The calculator shows 0.(9) as 1.
What is a mixed number?
A whole number plus a proper fraction. 2.75 is 11/4 as an improper fraction and 2 3/4 as a mixed number. The calculator shows both when the value is greater than 1 or less than −1.
Can I convert 0.333 (without brackets) to 1/3?
No, because 0.333 is exactly 333/1000. Only the infinitely repeating decimal 0.(3) equals 1/3. If your decimal was rounded, enter it with brackets to get the intended fraction.
Are the results exact?
Yes. The calculator works with whole-number arithmetic on the digits you type, not floating-point numbers, so long inputs are not rounded.
Does it work with negative numbers, commas and scientific notation?
Yes. Start with a minus sign for negative values. A single comma is accepted as the decimal mark, so 0,75 works the same as 0.75. Scientific notation such as 1e-7 or 2.5E3 is converted exactly. Do not use thousands separators or spaces: type 1234.5, not 1,234.5 or 1 234.5.