# Recurring Proof Note $4$

I'll prove that:

$y = 0.\overline{x_1x_2} =$$\frac{x_1x_2}{99}$

Let:

$y = 0.\overline{x_1x_2}$

$10y = x_1.\overline{x_2x_1}$

$100y = x_1x_2.\overline{x_1x_2}$

$100y - y = 99y$

$x_1x_2.\overline{x_1x_2} - 0.\overline{x_1x_2} = x_1x_2$

$99y = x_1x_2$

$\frac{99y}{99}$ $=$ $\frac{x_1x_2}{99}$

$y =$$\frac{x_1x_2}{99}$

Therefore, $y = 0.\overline{x_1x_2} =$$\frac{x_1x_2}{99}$ Note by Yajat Shamji
1 year, 2 months ago

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