what is equivalent to 0.51 when the 1 is being repeated

Let x = .51111111....

10x = 5.11111111

100x= 51.1111111

100x - 10x = 90x   = 51.1111111...-5.11111111.....

                     90x = 46

                         x = 46/90 = 23/45

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Thanks, EP....here's another method

Write the non-repeating part and repeating part without a decimal  =  51      (1) 

Subtract the non-repeating part  from (1).....51 - 5  =  46

Write this over a digit that has the same number of 9's as the repeating part and append to this the same number of 0's as the non-repeating part  =  90

So....we have  46 / 90   = 23 / 45