+0  
 
0
181
4
avatar+8 

How do I proceed writing 2,888... as a rational number?

elkster  Mar 28, 2017
Sort: 

4+0 Answers

 #1
avatar+79835 
+2

2.888888....  =

 

2 + 8/9  =

 

26 / 9

 

 

 cool cool‚Äč cool

CPhill  Mar 28, 2017
 #2
avatar+8 
0

Hmm, I see. But what is the step to turn 0,888... into 8/9 and furthermore into 26/9? I just can't see it...

 

Many thanks.

elkster  Mar 28, 2017
 #3
avatar+79835 
+2

OK

 

Forget about the "2"    we'll append that later

 

Since we have one repeated "8"....put this over the same number of "9's"  as repeated digits.....since we have one repeated digit....put the 8 over one 9    and we have    8/9

 

Add back the 2   and we have   2 8/9  =  26 / 9

 

 

Another approach

 

Let x = .8888....

And 10x  = 8.8888....so.....

 10x - x  =  8.8888 - .8888

 

9x  =  8      divide both sides by  9

 

x  = 8/9

 

Add back the 2 and we have   2 + 8/9  =  26/9

 

 

cool cool cool

CPhill  Mar 28, 2017
 #4
avatar+8 
+1

Brilliant. Thank you @CPhill - made my evening!

elkster  Mar 28, 2017

17 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details