2 ms·
> Others such as 7, 11, 13, 31 are shorter ⅐ has maximum possible length of n-1 (142857) > to see if e.g. telephone numbers could be represented as fractions
by Someone 3y ago
> Others such as 7, 11, 13, 31 are shorter
⅐ has maximum possible length of n-1 (142857)
> to see if e.g. telephone numbers could be represented as fractions yielding repeating decimals.
Every number can. For example, phone number 15224787 would yield
n = 0.1522478715224787[15224787]
⇒ n × 10⁸ = 15224787.1522478715224787[15224787]
= 15224787 + n
⇒ n × (10⁸ - 1) = 15224787
⇒ n = 15224787 / 99999999
= 1691643 / 11111111
(I didn’t check whether further simplifications are possible)
- m3047 3y agoYes: "the Nines". ;-) You didn't choose something which is prime. Primes end up being the number over the requisite number of Nines (and can't be simplified). The point of my game was to find simplifications. That's how I ended up asking myself "how can I predict how long a repeating decimal is?" and backed into the observation about 1/17 and its ilk. 3 is trivial because 9 is 3^2. 7 is a trick question because it happens to coincidentally be a factor of 999999. At my current rate of progress with this hobby, I might have something interesting to report in another decade or so.