Question

20 pontos!!!
Determine as frações geratrizes das seguintes dízimas periódicas:
A) 0,111...

B) 5,020202...

C) 12, 34222...

D) 2,777...

E) 1,710710710...

F) 0,1232323...

Answer 1

A) 0,111... = $\frac{1}{9}$
B) 5,020202... = 5 + 0,020202... = 5 + $\frac{2}{9}$ = $\frac{(9.5)+2}{9}$ = $\frac{45+2}{9}$ = $\frac{47}{9}$
C) 12,34222... = $\frac{12342-1234}{900}$ = $\frac{11108}{900}$ 
D) 2,777... = 2 + 0,777... = 2 + $\frac{7}{9}$ = $\frac{(9.2)+7}{9}$ = $\frac{18+7}{9}$ = $\frac{25}{9}$
E) 1,710710710... = 1 + 0,710710710... = 1 + $\frac{710}{999}$ = $\frac{(999.1)+710}{999}$ = $\frac{999+710}{999}$ = $\frac{1709}{999}$
F) 0,12323232... = $\frac{1232-12}{9900}$ = $\frac{1220}{9900}$

Answer 2

Resposta:

A Explicação passo-a-passo: