Question 381927
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Let *[tex \Large x = 0.\overline{124}]


Multiply it by 1000 (so that the decimal point falls where the repetition starts):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1000x\ =\ 124.\overline{124}]


Subtract x


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1000x\ -\ x\ =\ 124.\overline{124}\ -\ 0.\overline{124}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 999x\ =\ 124]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{124}{999}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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