Repeating decimals
Convert 0.333…, 0.1666… or 0.142857… exactly, using parentheses, a repeat field or trailing dots.
Free maths tool · Exact answers
Decimal to Fraction Calculator Repeating Decimals, Mixed Numbers, Inches & Step-by-Step
Turn any decimal into a simplified fraction or mixed number, including repeating decimals like 0.333… and percentages. This free decimal to fraction calculator shows every step, converts fractions back to decimals and finds the nearest 1/16 or 1/32 inch for measuring.
- Handles repeating decimals
- Step-by-step working
- Nearest inch fractions
Decimal to fraction calculator
For repeating decimals type 0.(3) or 0.1(6), or 0.333.... Add % for percentages.
Fraction or mixed number
Round to the nearest
Great for tape measures and drill bits. Try 3.14159 with a large denominator to find 355/113.
As a fraction
2.875 =238
As a mixed number: 2 7/8
- Mixed number
- 2 7/8
- Decimal
- 2.875
- Percent
- 287.5%
- Simplified from
- 2875/1000
Position on a 1-inch ruler
Step-by-step working
Closest fractions (continued fractions)
| Fraction | Decimal | Error |
|---|
Equivalent fractions
Features
A decimal to fraction calculator that does it all
Most converters stop at simple decimals. This one handles repeating decimals, percents, mixed numbers and measurements, and always shows how it got the answer.
Every step shown
See the place-value method or the algebra method for repeating decimals, line by line, ready for homework.
Nearest inch fraction
Round any decimal to the nearest 1/8, 1/16, 1/32 or 1/64, see it on a ruler and check the error in millimetres.
Works in reverse
Turn fractions and mixed numbers into decimals and percents, with repeating digits marked by a bar.
Percent to fraction
Type a value like 12.5% and get 1/8 instantly, along with the decimal and mixed-number forms.
Exact, even for long inputs
Big-number arithmetic keeps results exact for long decimals, and continued fractions find the best approximations.
How to use
How to use the decimal to fraction calculator
Choose a mode
Pick decimal to fraction, fraction to decimal, or nearest fraction for measurements.
Type your number
Enter a decimal, a percent, or a repeating decimal using brackets around the repeating part.
Read the answer
See the simplified fraction, mixed number, decimal and percent update as you type.
Check the steps
Follow the working below the result, then copy the answer with one click.
Learn
How to convert a decimal to a fraction
There are two methods, depending on whether the decimal ends or repeats forever.
Terminating decimals
Count the decimal places, write the digits over 10, 100, 1000 and so on, then divide top and bottom by their greatest common divisor.
0.75 = 75/100 = 3/4Repeating decimals
Call the number x, multiply by a power of 10 to line up the repeating part, and subtract to make it disappear.
10x − x = 3 → x = 1/3Mixed numbers
Convert the part after the decimal point, then put the whole number in front. 2.875 becomes 2 and 7/8.
2.875 = 2 7/8 = 23/8Percents
Drop the percent sign and divide by 100 first, then simplify the fraction as usual.
12.5% = 12.5/100 = 1/8Fraction to decimal
Divide the numerator by the denominator. If a remainder repeats, the digits repeat too.
3 ÷ 8 = 0.375Irrational numbers
Numbers like π never end or repeat, so they have no exact fraction. Continued fractions give the best approximations.
π ≈ 22/7 ≈ 355/113Chart
Decimal to fraction chart
Common decimals and their fraction equivalents, including the sixteenths used on rulers and tape measures.
| Decimal | Fraction | Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|---|---|
| 0.0625 | 1/16 | 0.5625 | 9/16 | 0.2 | 1/5 |
| 0.125 | 1/8 | 0.625 | 5/8 | 0.4 | 2/5 |
| 0.1875 | 3/16 | 0.6875 | 11/16 | 0.6 | 3/5 |
| 0.25 | 1/4 | 0.75 | 3/4 | 0.8 | 4/5 |
| 0.3125 | 5/16 | 0.8125 | 13/16 | 0.3 | 1/3 |
| 0.375 | 3/8 | 0.875 | 7/8 | 0.6 | 2/3 |
| 0.4375 | 7/16 | 0.9375 | 15/16 | 0.16 | 1/6 |
| 0.5 | 1/2 | 0.1 | 1/10 | 0.83 | 5/6 |
Who it helps
Where decimal to fraction conversion matters
Students and teachers
Check homework and see the method for both terminating and repeating decimals.
Woodworking and DIY
Turn digital caliper readings into the nearest 1/16 or 1/32 inch on your tape measure.
Cooking and baking
Convert scaled recipe amounts like 0.375 cup into 3/8 cup for your measuring set.
Engineering and machining
Match decimal drawings to fractional drill bits and stock sizes in seconds.
Finance and odds
Express rates and probabilities as simple fractions that are easier to explain.
Programmers
Find exact rational values behind floating-point numbers and check rounding errors.
FAQ
Decimal to fraction FAQ
How do you convert a decimal to a fraction?
Count the digits after the decimal point, write the number over 10, 100, 1000 and so on to match, then simplify. For example, 0.75 has two decimal places, so it becomes 75/100, and dividing both by 25 gives 3/4.
How do you convert a repeating decimal to a fraction?
Set the number equal to x, multiply by a power of 10 so the repeating part lines up, and subtract to cancel it. For 0.333…, 10x − x = 3, so x = 3/9 = 1/3. For 0.1666…, 100x − 10x = 15, so x = 15/90 = 1/6.
What is 0.375 as a fraction?
0.375 equals 375/1000. Dividing top and bottom by 125 gives 3/8, which is also 6/16 on a ruler.
What is 0.625 as a fraction?
0.625 equals 625/1000, which simplifies to 5/8 when you divide both numbers by 125.
How do I write a decimal as a mixed number?
Keep the whole-number part and convert only the digits after the decimal point. For 2.875, the 0.875 becomes 7/8, so the mixed number is 2 7/8, or 23/8 as an improper fraction.
How do I convert a decimal to the nearest 1/16 inch?
Multiply the decimal by 16, round to the nearest whole number, and put it over 16. For 0.3 inch, 0.3 × 16 = 4.8, which rounds to 5, so the nearest sixteenth is 5/16 inch.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/8 is 3 ÷ 8 = 0.375. Some fractions, like 1/3, never end, so the digits repeat forever as 0.333…
Can every decimal be written as a fraction?
Every decimal that ends or repeats can be written exactly as a fraction. Decimals that go on forever without repeating, such as pi, are irrational, so they can only be approximated, for example by 22/7 or 355/113.
Exact fractions, every time
Use the decimal to fraction calculator for homework, recipes or the workshop, and see the working behind every answer. For more maths help, explore our free online tools.
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