About the Fraction to Decimal Calculator
This fraction to decimal calculator divides the numerator by the denominator using exact long division, so instead of a rounded calculator answer you see the true decimal expansion. Terminating fractions such as 3/8 give an exact result (0.375); repeating fractions such as 5/6 show exactly which digits repeat, written as 0.8(3) and with a bar over the repeating block (0.83̅).
Enter an optional whole number to convert a mixed number like 2 3/4, and negative fractions work too. Alongside the decimal you get the simplified fraction, the percentage, the length of the repeating cycle and a rounded value to the number of decimal places you choose — handy for homework, recipes, measurements and checking spreadsheet results.
A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5; any other factor (3, 7, 11, …) makes the decimal repeat forever. The calculator tells you which case you have and why.
How to use the fraction to decimal calculator
- 1For a mixed number, enter the whole number; otherwise leave it at 0.
- 2Enter the numerator and the denominator.
- 3Read the exact decimal — digits in brackets repeat forever.
- 4Choose how many decimal places you want for the rounded value.
Formula and method
The calculator first turns a mixed number w n/d into the improper fraction (w × d + n)/d and reduces it to lowest terms. It then performs long division: at each step the remainder is multiplied by 10, divided by the denominator to give the next digit, and the new remainder carried forward.
Because there are only b possible remainders, they must either reach 0 (a terminating decimal) or eventually repeat. The calculator records every remainder; the first time one appears again, the digits produced since its first appearance are the repeating block, shown in brackets or with a bar.
- a
- Numerator (including the whole part for mixed numbers)
- b
- Denominator, in lowest terms
- ( ) or ‾
- Marks the digits that repeat forever
Worked examples
5/6 — a repeating decimal
5 ÷ 6: 50 ÷ 6 = 8 remainder 2, then 20 ÷ 6 = 3 remainder 2 again. The remainder 2 repeats, so the 3 repeats forever: 5/6 = 0.8333… = 0.8(3).
3/8 — a terminating decimal
8 = 2³ has only the prime factor 2, so the decimal must end. 3 ÷ 8 = 0.375, which is 37.5%.
Mixed number 2 3/7
2 3/7 = 17/7. Dividing by 7 cycles through all six non-zero remainders, so the block 428571 repeats: 2.428571428571…
Simplify first: 14/12
14/12 reduces to 7/6. 7 ÷ 6 = 1 remainder 1, then 10 ÷ 6 = 1 remainder 4, then 40 ÷ 6 = 6 remainder 4 repeating, so the answer is 1.1666… = 1.1(6).
Frequently asked questions
How do you convert a fraction to a decimal?+
Divide the numerator by the denominator. For 3/4 that is 3 ÷ 4 = 0.75. With long division you add a decimal point and zeros to the numerator and keep dividing until the remainder is 0 or starts repeating.
How do I know if a fraction gives a repeating decimal?+
Reduce the fraction to lowest terms and factor the denominator. If its only prime factors are 2 and 5 the decimal terminates; any other prime factor, such as 3, 7 or 11, makes it repeat.
What is 1/3 as a decimal?+
1/3 = 0.3333…, written 0.(3) or 0.3 with a bar over the 3. Rounded to two places it is 0.33, but the exact value has infinitely many 3s.
How do you convert a mixed number to a decimal?+
Convert the fraction part and add the whole number: 2 3/4 = 2 + 0.75 = 2.75. Equivalently, turn it into an improper fraction (11/4) and divide.
How long can the repeating part be?+
For a denominator d in lowest terms, the repeating block has at most d − 1 digits. 1/7 repeats every 6 digits, 1/17 every 16 and 1/97 every 96 digits.