A decimal expansion is not decided by how large a fraction looks or by a rounded calculator display. First reduce the rational number to lowest terms. In base ten, the only prime factors available in powers of ten are 2 and 5 because 10 = 2 × 5. A reduced denominator built only from those primes can be scaled to 10, 100, 1000, or another power of ten and therefore terminates. If any other prime factor remains, long division eventually repeats a remainder and the decimal is periodic.
Reduce before examining the denominator
The classification belongs to the value, not to one unreduced spelling. For example, 3/6 has denominator 6 = 2 × 3, which appears to contain the repeating factor 3. But 3/6 reduces to 1/2, and the factor 3 cancels completely. The reduced denominator 2 divides a power of ten, so the exact decimal is 0.5. FractionCalc always normalizes first. This prevents an unreduced common factor from causing a false repeating label and gives every equivalent input the same classification.
Remove factors of 2 and 5 exactly
Take 5/8. The reduced denominator is 8 = 2³, so no factor outside 2 or 5 remains. Multiply numerator and denominator by 125 to obtain 625/1000, hence the exact decimal 0.625. By contrast, 1/3 has reduced denominator 3. No power of ten is divisible by 3, so division produces 0.333… with a repeating 3. The classification can be made with exact integer division alone; binary floating point is neither necessary nor allowed to decide whether the expansion terminates.
Separate an exact decimal from a bounded preview
A terminating decimal can be emitted completely because its required number of places is finite and known from the powers of 2 and 5. A repeating decimal has no final digit. FractionCalc labels it as repeating and may show a bounded preview for orientation, but the exact result remains the reduced fraction. The ellipsis and classification are part of the answer, not decoration. A percent derived from a repeating value is also repeating unless displayed with an explicit approximation mark. Never copy a truncated decimal as though it were equal to the rational number.