vanitamaep315my vanitamaep315my

10-06-2019
Mathematics

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How do you convert 3.16 (6 repeating) to a fraction?

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LammettHash LammettHash

10-06-2019

Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].

Now,

[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]

[tex]\implies90x=285[/tex]

[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]

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