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.
DeWayfarer · 61-69, M
It's why the Sumerians used the Sexagesimal number system, base 60! The same base as clocks.
The larger the base the fewer the repeating numbers.
It goes by factorials by the way:
1x2x3x5x7 = 210.
So base 210 would be the most accurate for up to division by 7. Add a 11 to the factor then division by 11 would be accurate. Factorials of prime numbers.
The larger the base the fewer the repeating numbers.
It goes by factorials by the way:
1x2x3x5x7 = 210.
So base 210 would be the most accurate for up to division by 7. Add a 11 to the factor then division by 11 would be accurate. Factorials of prime numbers.
Lilnonames · F
tenente · 100+, M
AST!!!!!!!!!!!!
