#1**+2 **

Let x = .51111111....

10x = 5.11111111

100x= 51.1111111

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

90x = 46

x = 46/90 = 23/45

..

ElectricPavlov Nov 30, 2018

#2**+1 **

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

CPhill Dec 1, 2018