Long Division to Decimal

This fraction to decimal converter performs exact long division. Every rational number either terminates or enters a repeating pattern: the calculator detects the repeat by tracking remainders — when a remainder recurs, the digit cycle repeats forever, shown with an overline.

Why Some Decimals Repeat

The decimal terminates only when the denominator's prime factors are 2 and 5 (the factors of 10). A denominator like 7 or 3 introduces a repetend: 1/7 = 0.142857142857…, where the six-digit block cycles indefinitely.

Simplification First

Reducing the fraction with the GCD before converting doesn't change the value, but it makes the pattern easier to read — 4/6 simplifies to 2/3 = 0.6̅, and the simplified form is shown alongside the original.