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?

27*37 = 999

1/999 = .001001001001...

To get other examples would require numbers that produce other strings of nines like 369*271=99999

1/369 = .002710027100271...

1/271 = .002690036900369...

It is less distinct with smaller examples 11*9 = 99

1/9 = .11 11 11... (spaces for clarification)

1/11 = .09 09 09...

-Jer

Posted by Jer on 2004-11-24 14:40:25