Prove algebraically that 0.5 recurring =5/9 use x in working

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13-04-2018
Mathematics

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Prove algebraically that 0.5 recurring =5/9 use x in working

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LammettHash LammettHash · Answer 1 · 2018-04-13T18:37:14+02:00

LammettHash LammettHash

13-04-2018

Suppose [tex]x=0.555\ldots[/tex]. Then [tex]10x=5.555\ldots[/tex]. Subtracting [tex]x[/tex] from [tex]10x[/tex] will drop the fractional part:

[tex]10x-x=9x=5.555\ldots-0.555\ldots=5[/tex]

from which we immediately get [tex]x=\dfrac59[/tex].

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