Question

Qual a FRAÇÃO GERATRIZ de -4,6

Answer 1

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$\boxed{\begin{array}{l}\underline{\rm por~equac_{\!\!,}\tilde ao\!:}\\\sf x=4,666...\cdot10\\\sf 10x=46,666...\\-\underline{\begin{cases}\sf 10x=46,666\\\sf x=4,666...\end{cases}}\\\sf 9x=42\\\sf x=\dfrac{42\div3}{9\div3}\\\sf x=\dfrac{14}{3}\\\sf logo~-4,666...=-\dfrac{14}{3}\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm pela~soma~dos~termos~da~PG~infinita:}\\\sf 4,666...=4+\underbrace{\sf0,66...+0,0066...+0,0000666...}_{soma~dos~termos~da~PG~infinita}\\\sf a_1=0,66=\dfrac{66}{100}\\\sf a_2=\dfrac{66}{10000}\\\sf q=\dfrac{a_2}{a_1}\\\\\sf q=\dfrac{\frac{66}{10000}}{\frac{66}{100}}\\\\\sf q=\dfrac{66}{10000}\cdot\dfrac{100}{66}=\dfrac{1}{100}\end{array}}$

$\boxed{\begin{array}{l}\sf S_n=\dfrac{a_1}{1-q}\\\sf S_n=\dfrac{\frac{66}{100}}{1-\frac{1}{100}}\\\sf S_n=\dfrac{\frac{66}{100}}{\frac{99}{100}}\\\sf S_n=\dfrac{66}{100}\cdot\dfrac{100}{99}=\dfrac{66\div33}{99\div33}=\dfrac{2}{3}\\\\\sf 4,666...=4+\dfrac{2}{3}=\dfrac{14}{3}\\\\\sf logo~-4,666...=-\dfrac{14}{3}\end{array}}$

Answer 2

_______________

x = 4,666...

10x = 46,666...

10x - x = 46,666... - 4,6.666

9x = 42

x = 42/9

x = 14/3

x = -14/3

______________

Resposta:

-14/3

______________

Att: MarcosPCV