Question

Encontre a fração geratriz de cada dizima periodica a seguir

0,272727...

-0,777...

-3,111...

Answer 1

Explicação passo-a-passo:

$0,272727\dots=\dfrac{27}{99}=\dfrac{3}{11}$

$x=0,272727\dots$

$100x=27,272727\dots$

$100x-x=27,272727\dots-0,272727\dots$

$99x=27$

$x=\dfrac{27}{99}=\dfrac{3}{11}$

$-0,777\dots=\dfrac{-7}{9}$

$x=-0,777\dots$

$10x=-7,777\dors$

$10x-x=-7,777\dots-(-0,777\dots)$

$9x=-7,777\dots+0,777\dots$

$9x=7$

$x=\dfrac{7}{9}$

$-3,111\dots=-\dfrac{28}{9}$

$x=-3,111\dots$

$10x=-31,111\dots$

$10x-x=-31,111\dots-(-3,111\dots)$

$9x=-31,111\dots+3,111\dots$

$9x=-28$

$x=-\dfrac{28}{9}$