5 ms·
> In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. doesn't 1/6 use a prime factor of 2 as wel
by jayceekay 11y ago
> In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7.
doesn't 1/6 use a prime factor of 2 as well?
- thedufer 11y agoYes, but in order to have a non-repeating decimal expansion, the denominator must share _all_ of its factors with the base. That is, only fractions that, when reduced, have a denominator of the form 2^n*5^m (for natural numbers n, m) will terminate in base 10. The explanation given could probably be clearer.
- deleted 11y ago[deleted]
- jayceekay 11y agoah yes, the _all_ is what i missed. thanks.
- such_a_casual 11y agoIn the fraction 1/6, the prime factors of the denominator are 2 and 3. A base 10 number system has the 2 but not the 3.
- jayceekay 11y agogot it, thanks!