Repeating Decimal to Fraction Calculator

About this calculator

Every repeating decimal is secretly a rational number, and there is a standard algebraic trick to recover the exact fraction: let x equal the decimal, multiply x by a power of 10 large enough to shift one full repeating block past the decimal point, subtract the original x, and the repeating parts cancel out completely, leaving a simple equation to solve for x as a fraction. For example, x = 0.1666... gives 10x = 1.666..., and subtracting x from 10x cancels the repeating 6s, leaving 9x = 1.5, so x = 1/6.

This calculator automates that shift-and-subtract method for any decimal made of a whole part, optional non-repeating digits, and a repeating block, returning the exact reduced fraction rather than a rounded approximation. It is a standard topic in algebra courses covering rational numbers, and it matters practically anywhere an exact value is needed instead of a decimal that has been silently truncated — for instance confirming that 0.333... really does equal exactly 1/3 and not just a very close approximation.

Enter the whole part, any non-repeating digits, and the repeating block, and the calculator returns the exact fraction in lowest terms.