Show that 0.142857142857... =1 7 - Vidyadip

Question

Show that 0.142857142857... $=\frac{1}{7}$

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Answer

Let $x = 0.142857142857... (i)$
$\therefore1000000\text{x}=142857.\overline{142857}\ (\text{ii})$
Subtracting $(i)$ from $(ii)$, we get
$999999x = 142857 (iii)$
$\Rightarrow\text{x}=\frac{142857}{999999}=\frac{1}{7}$
Hence, $0.142857142857... =\frac{1}{7}$

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