# Recurring Proof Note $3$

I'll prove that:

$y = 0.0\overline{x_1}$ $=$ $\frac{x_1}{90}$

Let:

$y = 0.0\overline{x_1}$

$10y = 0.\overline{x_1}$

$100y = x_1.\overline{x_1}$

$100y - 10y = 90y$

$x_1.\overline{x_1} - 0.\overline{x_1} = x_1$

$90y = x_1$

$\frac{90y}{90}$ $=$ $\frac{x_1}{90}$

$y =$$\frac{x_1}{90}$

Therefore, $y = 0.0\overline{x_1}$ $=$ $\frac{x_1}{90}$

Note by Yajat Shamji
1 year, 2 months ago

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