All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution more fun and a reason | Comment 6 of 14 |

Note that 27*37 = 999
1000/27 = 37+1/27 = 37.037037...
1000 = 1mod(27)  and also =1mod(37)
The situation will hold true whenever you have two numbers N and M such that:
10^k is 1 both mod(N) and mod(M)
  or  N*M = 10^k - 1

9999=9*1111
1/9 = .11111111111...
1/1111 = .000900090009....

9999=99*101
1/99 = .01010101...
1/101 = .009900990099....

Trivial example:  9=3*3
1/3 = .33333333...

99999=271*369
1/271 = .003690036900369...
1/369 = .002710027100271...


  Posted by Larry on 2004-11-24 14:56:15
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information