## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# Classic puzzle: .9999..... AND 1

11 replies to this topic

### #11 ThunderCloud

ThunderCloud

• Members
• 102 posts
• Gender:Male
• Location:New England

Posted 05 November 2013 - 10:26 PM

well, not entirely sure i agree. for example, how would you denote 1/13?

you need a consistent way of denoting any rational number, not just ones that repeat the last digit.

personally, i like the bar method, where the repeated values have a bar over the top over the length of the repeating part.

so

```  _
0.9 = 1
```

would be more accurate (although more cumbersome.)

______

1/13 = 0.076923

The bar covers the part that repeats.

here's my challenge for you.

accurately add 1/13 to 45/89 in decimal representation.

This can be done, but would be rather tedious (particularly as the decimal expansion for 45/89 has a relatively long repeating digit string). The sum will also have a repeating pattern, of some size less than or equal to the LCM of the repeating digit string lengths of the two operands.

• 0

### #12 ThunderCloud

ThunderCloud

• Members
• 102 posts
• Gender:Male
• Location:New England

Posted 05 November 2013 - 11:45 PM

well, not entirely sure i agree. for example, how would you denote 1/13?

you need a consistent way of denoting any rational number, not just ones that repeat the last digit.

personally, i like the bar method, where the repeated values have a bar over the top over the length of the repeating part.

so

```  _
0.9 = 1
```

would be more accurate (although more cumbersome.)

I might have missed the gist of this question the first time around...

Another way to express 1/13 is 0.076923076923076923...

It is clumsy compared with the bar method in this example (unlike .999...), but still understandable.

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users