What is 0.8616161616161.... (61 recurring) as a fraction? (and how exactly do you figure it out)

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jamoo1762 jamoo1762

09-10-2017
Mathematics

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What is 0.8616161616161.... (61 recurring) as a fraction? (and how exactly do you figure it out)

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LammettHash LammettHash · Answer 1 · 2017-10-09T19:06:56+02:00

LammettHash LammettHash

09-10-2017

[tex]x=0.8616161\ldots=0.8\overline{61}[/tex]
[tex]10x=8.\overline{61}[/tex]
[tex]1000x=861.\overline{61}[/tex]

[tex]1000x-10x=861.\overline{61}-8.\overline{61}[/tex]
[tex]990x=853[/tex]
[tex]x=\dfrac{853}{990}[/tex]

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