Why Base 10 Decides

The terminate-or-repeat rule traces back to our base: 10 = 2 × 5. A decimal terminates only when the denominator's primes are limited to those same 2s and 5s. Change the base and you change which fractions end cleanly.

In base 12, for example, 1/3 = 0.4 and 1/4 = 0.3 — both exact, no repeating. That is the case for the duodecimal system: 12 has factors 2, 3, 4, and 6, so more everyday fractions terminate than in base 10.