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Find Friendly Fractions! (Posted on 2004-11-24) Difficulty: 2 of 5
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?

See The Solution Submitted by Old Original Oskar!    
Rating: 3.5455 (11 votes)

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Solution re: more fun and a reason | Comment 7 of 14 |
(In reply to more fun and a reason by Larry)

The number of digits in the repeating pattern are the same as the number of 9's in the product of the two friendly fractions.

Finding repeating patterns of 3-5 digits is not too difficult, but finding interesting divisors of 999999999 is a bit more difficult.

Edited on November 24, 2004, 4:07 pm

Edited on November 24, 2004, 5:18 pm
  Posted by Erik O. on 2004-11-24 16:07:25

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