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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2. can you explain how you got that?

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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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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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