What causes repeating decimals?
What causes some decimals to repeat, like 1/3=0.3333333333... and 2/3=0.6666666666... and in base 12 system 1/3 doesn't repeat but 1/5 in base 12 equals 0.249724972497...
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DrWatson · 70-79, M
The number 10 has two prime factors: 2 and 5. The only fractions (in lowest terms) with terminating decimals will be ones whose denominator contains only powers of 2 and/or powers of 5 as factors. So a base like 60 with more prime factors will have more terminating decimals. The number 12 has 3 and 2 as prime factors, which is why denominators which are powers of 3 give terminating decimals in that base.