Question

questão 2 -(PUC-RJ) A soma 1, 3333...+0,1666666...e igual a:

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Answer 1

Vamos là.

1.333... = 1 + 0.333...

x = 0,333...

10x = 3,333...

9x = 3

x = 1/3

1 + 1/3 = 4/3

0,1666.. = 0,1 + 0,0666...

y = 0,0666...

10y = 0,666...

100y = 6,666...

90y = 6

y = 6/90 = 1/15

1/10 + 1/15 = 15/150 + 10/150 = 25/150 = 1/6

1,333 + 0,1666... =  4/3 + 1/6 = 8/6 + 1/6 = 9/6 = 3/2