Question

A fração geratriz da dízima periódica 2,1777... 90/45 35/99 40/99

Answer 1

Resposta:

215,59/99

Explicação passo-a-passo:

x=2,1777*100

100x= 217,77

100x - x= 217,77 - 2,1777

99x = 215,59...

x = 215,59/99

Answer 2

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$\sf{x=2,17777...\cdot100}\\\sf{100x=217,777...\cdot10}\\\sf{1000x=2177,777...}$

$-\underline{\begin{cases}\sf{1000x=2177,\diagup\!\!\!7\diagup\!\!\!7\diagup\!\!\!7...}\\\sf{100x=217,\diagup\!\!\!7\diagup\!\!\!7\diagup\!\!\!7...}\end{cases}}$

$\sf{90\diagup\!\!\!0x=196\diagup\!\!\!0}\\\sf{x=\dfrac{196\div2}{90\div2}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=\dfrac{98}{45}}}}}}$