Repeating Decimal to Fraction Calculator

Split the number into the whole part, the non-repeating digits after the point, and the repeating block. Write the digits through one full repeat as a single number and subtract the digits that come before the repeat. Put that over a denominator made of one 9 for each repeating digit followed by one 0 for each non-repeating digit, then reduce. For example, 0.8333... becomes (83 minus 8) over 90, which simplifies to 5/6.

Apply the same method. With a repeating block of 9, the value 0.999... becomes 9 over 9, which reduces to exactly 1. This is not a rounding trick, because a repeating decimal and its fraction are two ways of writing the same number. The calculator returns 1 for that input.

The non-repeating digits sit right after the decimal point and appear only once, while the repeating block recurs forever. In 0.8333..., the 8 is non-repeating and the 3 repeats. In 0.41666..., the 41 is non-repeating and the 6 repeats. Enter each block in its own field so leading zeros, like the 0 in a repeating 09, are kept exactly.

Set the whole number to 0, leave the non-repeating field empty, and enter 142857 as the repeating block. The calculator returns 1/7, since 142857 over 999999 reduces to one seventh. Type only the digits of one full cycle, not the repeats, so use 142857 rather than 142857142857.

Yes. Any decimal that eventually repeats is a rational number, so it equals a ratio of two whole numbers. Terminating decimals count too, since you can treat the repeating block as 0, as in 0.5000... equals 1/2. Numbers that never repeat, such as pi or the square root of 2, are irrational and cannot be written as an exact fraction.

Yes. Choose the negative sign to convert values like minus 0.333..., which returns minus 1/3. When the digits add up to a whole number, such as 0.999... or 2.999..., the result shows as an integer like 1 or 3. Mixed numbers, like 1.5333... shown as 1 8/15, appear whenever the value is greater than 1.