Repeating Decimal to Fraction Calculator
Enter the non-repeating digits and repeating digits after the decimal point to convert to an exact fraction.
Last updated: September 5, 2026
Frequently asked questions
What is 0.1666... (0.1 with 6 repeating) as a fraction?
1/6 - with non-repeating digit "1" and repeating digit "6": numerator = 16 − 1 = 15, denominator = 100 − 10 = 90, and 15/90 simplifies to 1/6.
What is 0.333... (repeating 3) as a fraction?
1/3 - leave the non-repeating field empty and enter "3" as the repeating digit: numerator = 3 − 0 = 3, denominator = 10 − 1 = 9, and 3/9 simplifies to 1/3.
Why does the denominator use powers of 10?
Each decimal place represents a power of ten, so shifting the repeating block by its own length and subtracting cancels out the infinite repetition algebraically, leaving a finite fraction - the powers of 10 come directly from how many digits are in each part.
Does this work for decimals with no non-repeating part, like 0.727272...?
Yes - leave the non-repeating field empty and enter "72" as the repeating digits; the calculator treats a blank non-repeating part as zero digits.
How do I enter a decimal like 2.5555... that has a whole number part?
Enter just the decimal portion - non-repeating digits "5" would be wrong here since the 5 itself repeats, so leave non-repeating empty and enter "5" as repeating, getting 5/9, then add the whole number 2 separately to get 2 + 5/9 = 23/9.
What is 0.8333... (0.8 with 3 repeating) as a fraction?
5/6 - with non-repeating digit "8" and repeating digit "3": numerator = 83 − 8 = 75, denominator = 900 − 100 = 800... using the simpler rule (100−10)=90 for one repeating digit after one non-repeating digit: 75/90 simplifies to 5/6.
Can every repeating decimal be written as an exact fraction?
Yes - any decimal that eventually repeats forever is by definition a rational number, meaning it can always be expressed as a ratio of two integers. Only non-repeating, non-terminating decimals (like π) are irrational and can't be converted this way.