Repeating Decimal to Fraction Calculator

How it is calculated

The decimal is split into three parts typed as digit strings: the whole part W, the non-repeating digits (n digits long) and the repeating block (r digits long). The tool builds the fraction directly: denominator = (10r − 1) × 10n and numerator = (nonrepeating+repeating as one number) − (nonrepeating as a number) + W × denominator. It then divides both by their greatest common divisor, so the answer is in lowest terms. Leading zeros count as digits (0012 is four digits). The repeating block is required and, like the other parts, must contain only the digits 0 to 9; the whole part may be left empty for 0 and the non-repeating part may be empty. Negative numbers are not supported, so add the sign yourself afterwards. Very long entries (more than 18 digits across the non-repeating and repeating parts, or a result too large to print exactly) show no result rather than a rounded fraction.

Common mistakes

• Putting the repeating digits into the non-repeating box: for 0.1666… the 6 repeats, so 1 is non-repeating and 6 is the block; entering 16 as the block gives 16/99.
• Writing 0.3333 with four 3s as a repeating block of 3333: that is the same fraction 1/3, but a block of 3 is the shortest and clearest form.
• Dropping a leading zero in the non-repeating part: 0.0123123… needs non-repeating 0 and repeating 123 (giving 41/3,330); leaving out the zero gives 0.123123…, which is 41/333.
• Typing a decimal point or a minus sign in a box: each field takes digits only, and anything else shows no result.
• Expecting 0.999… to stay as a fraction below 1: the tool returns 1/1, since that repeating decimal equals 1 exactly.