Question

How to simplified 8/9

( please help I don’t understand this)

Answer 1

8/9 = 0.88
9 > 8
so first comes 0 in the quotient
then decimal comes so 8 becomes 80.
9×8=72
72-80=8
and then 8 comes recurring.

Answer 2

$\frac{8}{9} \\ \\ = \frac{8}{10} + \frac{8}{90} \\ \\ = \frac{8}{10} + \frac{8}{100} \times \frac{100}{90} \\ \\ = \frac{8}{10} + \frac{8}{100} \times \frac{10}{9} \\ \\ = \frac{8}{10} + \frac{8}{100}[1 + \frac{1}{9}] \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{900} \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} \times \frac{1000}{900}$

$\\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} \times \frac{10}{9} \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000}[1 + \frac{1}{9}] \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} + \frac{8}{9000} \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} + \frac{8}{10000} \times \frac{10000}{9000} \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} + \frac{8}{10000} \times \frac{10}{9} \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} + \frac{8}{10000}[1 + \frac{1}{9}]$

$\\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} + \frac{8}{10000} + \frac{8}{90000} \\ \\ \\ As\ this\ continues,\ It'll\ be\ endless. \\ \\ \\ \therefore\ \\ \\ \frac{8}{9} \\ \\ = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000} + \frac{8}{10000} + \frac{8}{100000} + ......... \\ \\ = 0.8 + 0.08 + 0.008 + 0.0008 + 0.00008 + ......... \\ \\ = 0.88888.........$

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