Pre-Calculus

Express the repeating decimal as a ratio of two integers.
1.23535353535...

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  1. 1223 / 990

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    posted by Bosnian
  2. can you explain how you got that?

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    posted by Sangita
  3. 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

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    posted by Reiny
  4. 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

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    posted by Bosnian

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