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# 2,888... into a rational number?

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228
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How do I proceed writing 2,888... as a rational number?

elkster  Mar 28, 2017
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#1
+83935
+2

2.888888....  =

2 + 8/9  =

26 / 9

​

CPhill  Mar 28, 2017
#2
+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
+83935
+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

CPhill  Mar 28, 2017
#4
+8
+1

Brilliant. Thank you @CPhill - made my evening!

elkster  Mar 28, 2017

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