Fraction to Decimal Converter | Spots Repeating Cycles and Shows Mixed Numbers

Type a decimal and get the reduced fraction. Type a fraction and get the decimal, expanded to five places. Enter 1/7 and the result shows 0.14285… (five digits with … because the long division does not terminate); enter 7/3 and the fraction card adds = 2 1/3 so you can read the mixed-number form at the same time.

💡 About this tool

Plain calculators usually truncate 1/7 to 0.142857142... and leave it to you to guess where the cycle starts and ends. This converter performs long division for five decimal places and shows those digits as-is, ending with … whenever the division does not terminate. The label under the decimal card (Repeating decimal / Terminating decimal / Integer) tells you which case you are looking at.

So 1/3 shows as 0.33333…, 1/7 as 0.14285…, and 1/6 as 0.16666… — five digits with … to signal that the same pattern keeps going. Going the other direction, type 0.625 and you get 5/8; type 10/8 and the tool reduces by the greatest common divisor to give 5/4, then notes the mixed form = 1 1/4 underneath. Everything updates as you type, so you can sweep through a whole homework page without clearing the box.

Repeating-decimal notation differs by country: English-language textbooks use a vinculum (overbar) 0.3̄, Japanese textbooks place a dot above the first and last digit of the cycle (0.3̇), Spanish-speaking textbooks often use an arc (0,3̂), and Russian/Polish textbooks use parentheses (0,(3)). This tool stays neutral and shows the raw digits — when writing the answer down, convert it to whichever convention your textbook uses.

The fraction card draws the result as a true stacked fraction — numerator above a horizontal bar above denominator, the standard math-textbook notation. Input still uses the typewriter form 5/8 because keyboards have no fraction key, but the display converts it to the proper barred form.

🧐 Frequently Asked Questions

Q. Can I type a mixed number directly, like 2 1/3? No. The input expects either a single fraction in numerator/denominator form or a decimal. Convert the mixed number to an improper fraction first (here, 7/3). The mixed-number form is then shown below the fraction card automatically.

Q. Does it support negative values? Yes. -3/4, -0.75, and 7/-3 are all accepted. The sign is normalised onto the numerator and rendered as a minus to the left of the stacked fraction, so 7/-3 is treated the same as -7/3.

Q. Can I use a comma as the decimal separator? Yes. 0,625 is treated the same as 0.625. The tool replaces the comma with a dot before parsing. Thousands separators are not supported, so do not type 1,234.5.

Q. What happens with fractions that have a very long period, such as 1/97? The decimal card displays the first five digits and appends … whenever the division does not terminate. 1/97 (period 96) shows as 0.01030…. Internally the tool keeps dividing up to 60 digits to decide whether the value is repeating or terminating, so the Repeating decimal label is still accurate even when the period is far longer than what fits on screen.

Q. What if I divide by zero or type something that is not a number? Inputs like 1/0, abc, or 1.2.3 are flagged as invalid. An error message appears under the input field and both result cards show a dash until you fix the value.

Q. Why does 1/2 show as 0.5 but 1/3 shows as 0.33333…? A fraction terminates only when the denominator (after reduction) has no prime factors other than 2 and 5. 1/2 and 1/8 terminate; 1/3, 1/7, and 1/11 do not, because 3, 7, and 11 are coprime to 10.

📚 Cyclic numbers and the surprising symmetry of 1/7

1/7 = 0.142857142857... is the textbook example of a cyclic number. Multiply 142857 by 2 and you get 285714; by 3 and you get 428571; by 4, 5, and 6 you get 571428, 714285, and 857142. Every product is the same six digits in the same cyclic order, just starting at a different position. This is not a coincidence: it happens because 7 is what number theorists call a full reptend prime in base 10, meaning its reciprocal uses every non-zero residue (1, 2, 3, 4, 5, 6) before returning to its starting point.

The same property shows up for 17, 19, 23, 29, 47, and 59 in base 10, which is why dividing 1 by any of them produces a period exactly one digit shorter than the denominator. For other primes the period can be much shorter than p − 1: 1/11 = 0.(09) has period 2, and 1/13 = 0.(076923) has period 6 instead of 12. Whether a prime is full-reptend in a given base is still an open question in number theory; the famous Artin's conjecture predicts how often this happens, but no one has proved it yet.

A nice party trick: multiply 142857 by 7. You get 999999, six nines in a row. That happens for every cyclic number, and it is the cleanest visual proof that 0.142857142857… really equals 1/7.