Decimal to Fraction Calculator
Type a decimal and get the exact fraction in lowest terms, the mixed number and the working. Repeating decimals like 0.1666... work, and you can round to the nearest 1/16, 1/32 or 1/64 for measurements.
- Repeating decimals
- Simplest form
- Nearest 1/16 or 1/64
- Step-by-step working
Decimal to convert
For a repeating decimal, put the repeating digits in brackets, 0.1(6), or type a few repeats and three dots, 0.1666.... Percentages (12.5%) and e-notation (1.5e-3) work too.
- Simplified fraction
- 5/8
- Decimal
- 0.625
- Percentage
- 62.5%
Step-by-step working
Write the decimal over a power of 10
0.625=625 over 1000There are 3 digits after the decimal point, so the denominator is 1 followed by 3 zeros.
Simplify by the greatest common factor
GCF(625, 1000) = 125625 over 1000=625 ÷ 125 over 1000 ÷ 125=5 over 8Divide the top and the bottom by the same number. The value does not change.
Exact arithmetic for numbers of any size, with no rounding errors. Everything runs in your browser, and nothing you type leaves this page.
How do you convert a decimal to a fraction?
Every terminating decimal is a fraction over a power of 10. 0.625 has three decimal places, so it is 625/1000, which simplifies to 5/8. Repeating decimals are fractions too: x = 0.333... means 10x = 3.333..., and subtracting gives 9x = 3, so x = 1/3. This converter does both. For a repeating decimal, put the repeating digits in brackets, 0.1(6), or type a few repeats followed by three dots, 0.1666..., and it works out the repeating block for you. It also rounds to the nearest 1/2, 1/4, 1/8, 1/16, 1/32, 1/64 or 1/100, which is handy for tape measures and drill bits.
How to convert a decimal to a fraction here
- Type the decimal, for example 0.625, 2.75 or −0.4. You can also type a percentage such as 12.5%.
- For a repeating decimal, write 0.(3) or 0.333... and 0.1(6) or 0.1666....
- Read the fraction in simplest form, the mixed number and the percentage.
- Optional: choose “Also round to the nearest” to get the closest 1/16 or 1/64 and how far off it is.
- Check the working: the power of 10, or the algebra that removes the repeating part, then the simplification.
Decimal to fraction rules
- 0.abc = abc/1000
- 0.625 = 625/1000 = 5/8.
- 0.(r) = r/(10ᵏ − 1)
- With k repeating digits: 0.(27) = 27/99 = 3/11.
- 0.a(r) = (ar − a)/(10ᵏ × (10ʲ − 1))
- 0.1(6) = (16 − 1)/90 = 15/90 = 1/6.
- Nearest 1/n = round(x × n)/n
- 0.3 to the nearest 1/16: round(4.8)/16 = 5/16.
Why use this decimal to fraction calculator
- Every step, freeThe full working is always on the page: common denominator, rewritten fractions, greatest common factor and the final simplification. No account, no premium tier and no daily limit.
- Exact answers at any sizeFractions are stored as exact whole numbers, so a 40-digit numerator stays exact. There is no floating-point rounding of the kind that turns 0.1 + 0.2 into 0.30000000000000004.
- Repeating decimals shown properly1/7 is shown as 0.142857 with a bar over the repeating block, instead of being cut off at 0.1428571429. You also get a rounded value to copy.
- Fast and privateThe answer updates as you type and is worked out on your device. Nothing you enter is sent to a server, and the calculator keeps working if your connection drops.
How it compares with other fraction calculators
| Feature | This calculator | Typical online calculators |
|---|---|---|
| More than two numbers in one problem | Yes, up to 10, with order of operations | Usually two |
| Fractions, mixed numbers, whole numbers and decimals together | Yes | Often separate calculators |
| Full step-by-step working | Always free | Often missing or behind a paywall |
| Repeating decimals | Exact, with a bar over the repeating digits | Rounded to a few places |
| Very large numbers | Exact at any size | Rounded or a separate big number tool |
| Decimal to fraction for repeating decimals | Type 0.1(6) or 0.1666... | Count the repeating digits yourself |
| Privacy | Runs in your browser, nothing sent | Inputs often sent to a server |
Fraction to decimal chart
Common fractions with their exact decimals and percentages. Sixteenths, thirty-seconds and sixty-fourths are the marks on an inch tape measure.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3 repeating | 33.3 repeating% |
| 2/3 | 0.6 repeating | 66.6 repeating% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.16 repeating | 16.6 repeating% |
| 5/6 | 0.83 repeating | 83.3 repeating% |
| 1/7 | 0.142857 repeating | 14.285714 repeating% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/9 | 0.1 repeating | 11.1 repeating% |
| 1/10 | 0.1 | 10% |
| 1/12 | 0.083 repeating | 8.3 repeating% |
| 5/12 | 0.416 repeating | 41.6 repeating% |
| 7/12 | 0.583 repeating | 58.3 repeating% |
| 1/16 | 0.0625 | 6.25% |
| 3/16 | 0.1875 | 18.75% |
| 5/16 | 0.3125 | 31.25% |
| 7/16 | 0.4375 | 43.75% |
| 9/16 | 0.5625 | 56.25% |
| 11/16 | 0.6875 | 68.75% |
| 13/16 | 0.8125 | 81.25% |
| 15/16 | 0.9375 | 93.75% |
| 1/32 | 0.03125 | 3.125% |
| 1/64 | 0.015625 | 1.5625% |
Common uses
- Tape measures and drill bits. Turn 0.3125 in into 5/16 in, or 2.71 in into the nearest 1/8.
- Recipes. Change 0.75 cup into 3/4 cup or 0.333 into 1/3.
- Math homework. Convert repeating decimals with the algebra written out.
- Spreadsheets. Turn a decimal result from Excel back into a clean fraction.
More math help: the percentage calculator for percent questions, the ratio calculator for simplifying and scaling ratios, and the math editor to type up your working as a neat equation.
Fraction words explained
- Numerator
- The top number. It counts how many parts you have.
- Denominator
- The bottom number. It says how many equal parts make one whole.
- Proper fraction
- The numerator is smaller than the denominator, such as 3/4.
- Improper fraction
- The numerator is as big as or bigger than the denominator, such as 7/4.
- Mixed number
- A whole number and a proper fraction together, such as 1 3/4.
- Equivalent fractions
- Different fractions with the same value, such as 1/2, 2/4 and 50/100.
- Least common denominator
- The smallest number all the denominators divide into.
- Greatest common factor
- The biggest number that divides both the numerator and the denominator.
- Reciprocal
- A fraction turned upside down. The reciprocal of 2/3 is 3/2.
- Repeating decimal
- A decimal whose digits repeat forever, such as 0.333... for 1/3.
For example, in 3 over 4 the numerator is 3 and the denominator is 4.
Worked examples: 0.625 and 0.1666...
0.625 has three digits after the point, so write it as 625/1000. The greatest common factor of 625 and 1000 is 125, and dividing both gives 5/8. For 0.1666..., let x = 0.1666.... Multiply by 100: 100x = 16.666.... Multiply by 10: 10x = 1.666.... Subtracting cancels the repeating 6s: 90x = 15, so x = 15/90 = 1/6.
What to expect from the result
Decimals up to 400 digits are converted exactly. A decimal you have already rounded, such as 0.33, gives the exact fraction for that rounded number (33/100), not 1/3; add three dots or brackets to say it repeats. The nearest 1/16 or 1/64 option rounds half up.
Decimal to Fraction Calculator questions
How do you convert a decimal to a fraction?
Write the digits after the point over 1 followed by as many zeros as there are digits, then simplify. 0.75 = 75/100 = 3/4, and 0.125 = 125/1000 = 1/8.
How do you convert a repeating decimal to a fraction?
Call the decimal x, multiply by a power of 10 to shift one repeating block, and subtract to cancel the repeats. For 0.272727..., 100x = 27.2727..., so 99x = 27 and x = 27/99 = 3/11.
What is 0.375 as a fraction?
0.375 = 375/1000. The GCF is 125, so it simplifies to 3/8.
What is 0.333... as a fraction?
0.333... repeating is exactly 1/3. If you mean 0.333 that stops, it is 333/1000.
How do I convert a decimal to a mixed number?
Convert the part after the point and keep the whole number. 2.75 = 2 + 75/100 = 2 + 3/4 = 2 3/4.
How do I convert a decimal to the nearest 1/16 inch?
Multiply by 16, round to the nearest whole number and put it over 16, then simplify. 0.3 × 16 = 4.8, which rounds to 5, so 0.3 in is about 5/16 in. Choose 1/16 in the rounding list to do this automatically.