Question

qual é a geratriz da dizima 1,003333?​

Answer 1

$\text{Denotando a dizima por x :}$

$x=1,\!003333\dots\implies x=1+\underbrace{0,\!003333\dots}_y$

$y=0,\!003333\dots\implies 100y=0,\!3333\dots~\land~1000y=3,\!3333\dots$

$\therefore$

$1000y-100y=3,\!3333...-0,33333...\iff$

$\iff 900y=3\iff$

$\iff y=\dfrac{3}{900}.$

$\therefore$

$x=1+\dfrac{3}{900}\implies$

$\implies x=\dfrac{900}{900}+\dfrac{3}{900}\implies$

$\implies x=\dfrac{900+3}{900}\implies$

$\implies \underline{\boxed{x=\dfrac{903}{900}}}\,.\leftarrow\text{geratriz procurada.}$