How to divide the denominator into parts

[Habil]

I was wondering if there was a way to manipulate 1/11 to something like a/10 +b/1. or any other manipulation that you guys know of. i came across it while trying to have fun with numbers and I am stuck

 

[Deleted member 4993]

I was wondering if there was a way to manipulate 1/11 to something like a/10 +b/1. or any other manipulation that you guys know of. i came across it while trying to have fun with numbers and I am stuck

Please post the EXACT problem as it was given to you.

You cannot split 11 into two positive-integer factors (other than 1 and 11).

 

[pka]

[imath]\dfrac{1}{11}=\displaystyle\sum\limits_{n = 1}^\infty {\frac{9}{{{{10}^{2n}}}}}=0.\overline{09}[/imath]

 

[Steven G]

1/11 = 1/10 +(1/11-1/10) = 1/10+ (10/110 -11/110) = 1/10 - 1/110

1/11 = 1/1 - 10/11