Recurring Proof Note 55

I'll prove that

y=0.x1x2=y = 0.x_1\overline{x_2} = x1x2x190\frac{x_1x_2 - x_1}{90}

Let:

y=0.x1x2y = 0.x_1\overline{x_2}

10y=x1.x210y = x_1.\overline{x_2}

10yy=9y10y - y = 9y

x1.x20.x1x2=x1.x2x1x_1.\overline{x_2} - 0.x_1\overline{x_2} = x_1.x_2 - x_1

9y=x1.x2x19y = x_1.x_2 - x_1

9y9\frac{9y}{9} == x1.x2x19\frac{x_1.x_2 - x_1}{9}

90y90\frac{90y}{90} == x1x2x190\frac{x_1x_2 - x_1}{90}

y=y = x1x2x190\frac{x_1x_2 - x_1}{90}

Therefore, y=0.x1x2=y = 0.x_1\overline{x_2} = x1x2x190\frac{x_1x_2 - x_1}{90}

Note by Yajat Shamji
1 year, 2 months ago

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