Question

Por favor me ajudem ​

Answer 1

1.

a) $1.444\dots$

$\mathrm{Seja}\ x=1.\overline{4}\Longrightarrow 10x=14.\overline{4}$

$\Longrightarrow 10x-x=14.\overline{4}-1.\overline{4}\Longrightarrow 9x=13\ \therefore\ \boxed{x=\dfrac{13}{9}}$

b) $0.333\dots$

$\mathrm{Seja}\ y=0.\overline{3}\Longrightarrow 10y=3.\overline{3}$

$\Longrightarrow 10y-y=3.\overline{3}-0.\overline{3}\Longrightarrow 9y=3\ \therefore\ \boxed{y=\dfrac{1}{3}}$

c) $4.181818\dots$

$\mathrm{Seja}\ z=4.\overline{18}\Longrightarrow 100z=418.\overline{18}$

$\Longrightarrow 100z-z=418.\overline{18}-4.\overline{18}\Longrightarrow 99z=414\ \therefore\ \boxed{z=\dfrac{46}{11}}$

2.

a) $3.1777\dots$

$\mathrm{Seja}\ a=3.1\overline{7}\Longrightarrow 10a=31.\overline{7}\Longrightarrow 100a=317.\overline{7}$

$100a-10a=317.\overline{7}-31.\overline{7}\Longrightarrow 90a=286\ \therefore\ \boxed{a=\dfrac{143}{45}}$

b) $0.7888\dots$

$\mathrm{Seja}\ b=0.7\overline{8}\Longrightarrow 10b=7.\overline{8}\Longrightarrow 100b=78.\overline{8}$

$100b-10b=78.\overline{8}-7.\overline{8}\Longrightarrow 90b=71\ \therefore\ \boxed{b=\dfrac{71}{90}}$

c) $41.3454545\dots$

$\mathrm{Seja}\ c=41.3\overline{45}\Longrightarrow 10c=413.\overline{45}\Longrightarrow 1000c=41345.\overline{45}$

$1000c-10c=41345.\overline{45}-413.\overline{45}\Longrightarrow 990c=40932\ \therefore\ \boxed{c=\dfrac{2274}{55}}$

Answer 2

Resposta:

1) a) 1,444... = 13/9  b) 0,333... = 3/9  c) 4,181818 =43/11

2) a) 3,1777... =16/9  b) 0,7888…=71/90 A C EU TBM NUM SEI

 

Explicação passo-a-passo: