Question
Show that 0.142857142857... $=\frac{1}{7}$
✓
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... $=\frac{1}{7}$
$\therefore1000000\text{x}=142857.\overline{142857}\ (\text{ii})$
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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