23 Sep
2006
23 Sep
'06
2 p.m.
Christian writes: << With a = 17537 = prime number, And b = 12800(...0) = 2^(9+k) * 5^(2+k), my last family produce always reduced fractions a/b, i.e. on (0, 1): 17537/128000 = 0.1370078125
Very nice example. Now I wonder if there's an example p/q in lowest terms, with 1/10 < p/q < 1, so that the most compact way of writing the decimal uses the same digits (with the same multiplicity). (By compact I mean no leading or trailing zeroes.) Okay, we can start with binary. How about a binary fraction p/q in lowest terms, 1/2 < p/q < 1, with its compact binary representation using the same number of 0's & 1's as there are in p_2 & q_2 (with multiplicity) ? --Dan