Question

encontre a fração geratriz das dízimas periódicas compostas a)0,30111 b)28,37919191 c)10,2300300300 d)91,351444​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{x = 0,3011}$

$\mathsf{10x = 30,11}$

$\mathsf{1000x = 301,1}$

$\mathsf{1000x - 100x = 301,11 - 30,11}$

$\mathsf{900x = 271}$

$\boxed{\boxed{\mathsf{x = \dfrac{271}{900}}}}\leftarrow\textsf{letra A}$

$\mathsf{x = 28,37919191}$

$\mathsf{100x = 2.837,919191}$

$\mathsf{10.000x = 283.791,9191}$

$\mathsf{10.000x - 100x = 283.791,9191 - 2.837,9191}$

$\mathsf{9.900x = 280.954}$

$\mathsf{x = \dfrac{280.954 \div 2}{9.900 \div 2}}$

$\boxed{\boxed{\mathsf{x = \dfrac{140.477}{4.950}}}}\leftarrow\textsf{letra B}$

$\mathsf{x = 10,2300300300}$

$\mathsf{10x = 102,300300300}$

$\mathsf{10.000x = 102.300,300300}$

$\mathsf{10.000x - 10x = 102.300,300300 - 102,300300}$

$\mathsf{9.990x = 102.198}$

$\mathsf{x = \dfrac{102.198 \div 6}{9.990 \div 6}}$

$\boxed{\boxed{\mathsf{x = \dfrac{17.033}{1.665}}}}\leftarrow\textsf{letra C}$

$\mathsf{x = 91,351444}$

$\mathsf{1.000x = 91.351,444}$

$\mathsf{10.000x = 913.514,44}$

$\mathsf{10.000x - 1.000x = 913.514,44 - 91.351,444 }$

$\mathsf{9.000x = 822.163}$

$\boxed{\boxed{\mathsf{x = \dfrac{822.163}{9.000}}}}\leftarrow\textsf{letra D}$