Asked by Sangita
                Express the repeating decimal as a ratio of two integers.
1.23535353535...
            
        1.23535353535...
Answers
                    Answered by
            Bosnian
            
    1223 / 990
    
                    Answered by
            Sangita
            
    can you explain how you got that?
    
                    Answered by
            Reiny
            
    here is one way...
let x = 1.23535353...
1000x= 1235.35353... (#1)
10x = 12.353535.. (#2)
subtract #1 - #2 :
990x = 1223
x = 1123/990 , the answer that Bosnian gave you
    
let x = 1.23535353...
1000x= 1235.35353... (#1)
10x = 12.353535.. (#2)
subtract #1 - #2 :
990x = 1223
x = 1123/990 , the answer that Bosnian gave you
                    Answered by
            Bosnian
            
    1 / 5 = 0.2
1 / 198 = 0.0050505050
7 * 1 / 198 = 7 / 198 = 0. 0353535
1.23535353535 = 1 + 1 / 5 + 7 / 198
198 * 5 = 990
1 = 990 / 990
1 / 5 = 1 * 198 / 990 = 198 / 990
7 / 198 = 5 * 7 / 990 = 35 / 990
1 + 1 / 5 + 7 / 198 =
990 / 990 + 198 / 990 + 35 / 990 =
1223 / 990
    
1 / 198 = 0.0050505050
7 * 1 / 198 = 7 / 198 = 0. 0353535
1.23535353535 = 1 + 1 / 5 + 7 / 198
198 * 5 = 990
1 = 990 / 990
1 / 5 = 1 * 198 / 990 = 198 / 990
7 / 198 = 5 * 7 / 990 = 35 / 990
1 + 1 / 5 + 7 / 198 =
990 / 990 + 198 / 990 + 35 / 990 =
1223 / 990
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