Can you explain the relationship between 27 and 37 that produces 1/27=0.037037037... and 1/37=0.027027027...? (That is, each number forms the other number's repeating decimal.)

Can you provide other similar examples, possibly with more or fewer digits?

1/37=27/999
1/27=37/999

which explains the repeating fractions for them.

Any 2 numbers that when multiplied together make a number 10^k-1 where k is an arbitrary integer will have this property.

Posted by The riddler on 2006-01-07 20:47:18