dada a dízima periódica diga de qualquer fração e a geratriz a)0,44444 b)0,12525 c)0,54545 d)0,04777
Soluções para a tarefa
Resposta:
A) 4/9
B) 124/990
C) 54/99
D) 43/900
Explicação passo-a-passo:
Resposta:
a)0,4444...
x = 0,4444... ➀
10 • x = 10 • 0,4444...
10x = 4,4444... ➁
➁ - ➀
10x = 4,4444...
– x = 0,4444...
9x = 4
x = 4
9
b) 0,12525...
x = 0,12525... ➀
10 • x = 10 • 0,12525...
10x = 1,2525... ➁
1000 • x = 1000 × 0,12525...
1000x = 125,2525... ➂
➂ - ➁
1000x = 125,2525...
– 10x = 1,2525...
990x = 124
x = 124
990
c)0,54545...
x = 0,54545... ➀
100 • x = 100 • 0,54545...
100x = 54,54545... ➁
➁ - ➀
100x = 54,54545...
– x = 0,54545...
99x = 54
x = 54
99
d)0,04777...
x = 0,04777... ➀
100 • x = 100 • 0,04777...
100x = 4,777... ➁
1000 • x = 1000 • 0,04777...
1000x = 47, 777... ➂
➂ - ➁
1000x = 47, 777...
– 100x = 4,777...
900x = 43
x = 43
900