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?

This is a prime of example of why mathematics is an applied science and an art form.

In this example, 1/37 and 1/27 produce their own reversible repeating decimals because 27*37 = 999 and 1000 - 999 = 1 which is the numerator once again. This phenomenon happens every time there are 2 fractions with common numerators and a remainder that is the numerator!

The lowest whole number example is 1/3 and 1/3. 3x3=9 and 10-9=1.

How about a cool, 1/7 and 1/142,857? 7*142,857 = 999,999 and 1,000,000-999,999 = 1!

Here's a large numerator example! 25/27 and 25/925. 27*925= 24,975 and 25,000-24,975 = 25!

How cool is this problem! :)

Edited on November 26, 2004, 2:59 pm

Edited on November 26, 2004, 3:12 pm

Posted by Michael on 2004-11-24 22:29:03