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?

  Submitted by Old Original Oskar!    
Rating: 3.5455 (11 votes)
Solution: (Hide)
Say 1/X=0.YYY.... If Y is n digits long, then the fraction equals Y times 10-n+10-2n+10-3n...= Y/(10n-1). Therefore, we need XY=10n-1. In our case, 27x37=103-1; other examples are 3x3=101-1 (1/3=0.333...) or 11x9=102-1 (1/11=0.090909...) and so on.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtssome thoughts ivK Sengupta2022-04-08 00:07:28
Some Thoughtssome thoughts iiiK Sengupta2022-04-07 07:20:06
some thoughts iiK Sengupta2022-04-06 12:25:00
re: ***************K Sengupta2008-04-29 11:24:04
some thoughtsK Sengupta2008-02-21 14:21:06
repeating fractionsThe riddler2006-01-07 20:47:18
re: 999999999999999Charlie2004-11-27 16:30:01
999999999999999sragen2004-11-27 06:14:14
SolutionExplanationMichael2004-11-24 22:29:03
re(2): more fun and a reasonCharlie2004-11-24 18:57:53
Solutionre: more fun and a reasonErik O.2004-11-24 16:07:25
Solutionmore fun and a reasonLarry2004-11-24 14:56:15
Cute...Erik O.2004-11-24 14:54:17
What you're getting at?Jer2004-11-24 14:40:25
Hints/TipsVery Slick, Oscarowl2004-11-24 14:23:50
Hints/Tipsmore examplesRandyOrton2004-11-24 13:15:02
more examplesRandyOrton2004-11-24 13:05:15
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 (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information