Fraction to Decimal Calculator
Turn any fraction or mixed number into an exact decimal and a percentage. Repeating decimals are shown with a bar over the digits that repeat, and the long division is laid out step by step.
- Exact repeating decimals
- Long division steps
- Percent too
- Conversion chart
Fraction to convert
Enter a fraction or mixed number. Repeating decimals are shown with a bar over the digits that repeat.
- Simplified fraction
- 7/12
- Decimal
- 0.583 repeating
- Percentage
- 58.3 repeating%
A bar over digits means they repeat forever. In plain text this is written 0.58(3).
Step-by-step working
Divide the numerator by the denominator
7 ÷ 12 = 0 remainder 77 × 10 = 70 70 ÷ 12 = 5 remainder 1010 × 10 = 100 100 ÷ 12 = 8 remainder 44 × 10 = 40 40 ÷ 12 = 3 remainder 4Answer:0.583 repeatingRemainder 4 has come up before, so the digits 3 repeat forever.
Why it repeats
Denominator 12 = 2² × 3In lowest terms, the denominator has a prime factor other than 2 or 5, so the decimal repeats.
As a percentage
0.583 repeating × 100 = 58.(3)%
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 fraction to a decimal?
A fraction is a division: 3/8 means 3 ÷ 8. Dividing the numerator by the denominator gives the decimal, 0.375. Some fractions stop (terminate), and some repeat forever, such as 1/3 = 0.333... or 1/7 = 0.142857142857.... A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5; anything else repeats. This converter does the long division exactly, finds where the repeating block starts and how long it is, and shows it with a bar, so 7/12 appears as 0.583 with a bar over the 3. It also gives the percentage and a rounded value you can paste into a spreadsheet.
How to convert a fraction to a decimal here
- Type the numerator and the denominator. For a mixed number such as 1 3/8, put the 1 in the left box.
- Read the decimal and the percentage. A bar over digits means they repeat forever.
- Follow the long division in the working: each remainder is multiplied by 10 and divided again until it is 0 or a remainder comes back.
- Copy the exact decimal or the value rounded to 10 places. Use the chart below for the common fractions.
Fraction to decimal rules
- n/d = n ÷ d
- 3/8 = 3 ÷ 8 = 0.375.
- Terminates if d = 2ᵃ × 5ᵇ
- 7/20 terminates (20 = 2² × 5); 5/6 repeats (6 has a factor 3).
- Percent = decimal × 100
- 0.375 × 100 = 37.5%.
- Mixed: w n/d = w + n ÷ d
- 2 3/4 = 2 + 0.75 = 2.75.
Why use this fraction to decimal 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
- Inch fractions. Turn 5/16 in into 0.3125 in for a drill chart or CAD drawing.
- Grades and scores. Convert 17/20 to 0.85 or 85%.
- Money and stock prices. Change 3/8 to 0.375 for a calculation or a spreadsheet.
- Math lessons. Show why 1/7 repeats and how long its repeating block is.
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 example: 7/12 as a decimal
7 ÷ 12 = 0 remainder 7. Bring down a zero: 70 ÷ 12 = 5 remainder 10. Then 100 ÷ 12 = 8 remainder 4, and 40 ÷ 12 = 3 remainder 4. The remainder 4 has come up again, so the digit 3 repeats forever. 7/12 = 0.58333..., written 0.583 with a bar over the 3, which is about 58.33%.
What to expect from the result
Repeating blocks are found exactly for up to 1,000 decimal places. Fractions such as 1/9967 have a repeating block thousands of digits long; for those the calculator shows the first 1,000 digits and a rounded value.
Fraction to Decimal Calculator questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. For a mixed number, convert the fraction part and add the whole number: 2 3/4 = 2.75.
How do I write a repeating decimal?
Put a bar (a vinculum) over the digits that repeat. 1/3 = 0.3 with a bar over the 3, and 1/7 = 0.142857 with a bar over all six digits. In plain text people often write 0.(3) or 0.333....
Which fractions give terminating decimals?
A fraction in lowest terms has a terminating decimal only if its denominator is made of the primes 2 and 5. 3/8, 7/20 and 9/25 terminate; 1/3, 5/6 and 2/7 repeat.
What is 1/3 as a decimal?
1/3 = 0.333... with the 3 repeating forever. Rounded to two places it is 0.33, and as a percentage it is 33.333...%.
How do I convert a fraction to a percentage?
Convert it to a decimal and multiply by 100. 3/8 = 0.375, which is 37.5%. The calculator shows the percentage with every answer.
What is 5/8 as a decimal?
5/8 = 0.625, or 62.5%. Eighths always end after three decimal places: 1/8 = 0.125, 3/8 = 0.375 and 7/8 = 0.875.