Question

sendo A=3,3 (dizima) B=0,6 (dizima) K=0,01 (dizima) e O=2/3 determine o valr da expressão AK/B+O

Answer 1

A= 3,333..

3,333... = x

33,333...= 10x

10x-x= 33,333- 3,333

9x= 30

x= 30/9 = 10/3

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A= 10/3

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B= 0,666...

0,666... = x

6,666...= 10x

10x-x= 6,666-0,666

9x= 6

x= 6/9 = 2/3

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B= 2/3

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K= 0,0111...

0,0111= x

1,111 = 100x

100x-x= 1,111 - 0,0111

99x= 1,1 ×(10)

990x= 11 (÷11)

90x=1

x= 1/90

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K= 1/90

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O= 2/3

Assim,

A.K/B + O =

( 10/3 × 1/90 ÷ 2/3 ) + 2/ =

(1/27 ÷ 2/3) + 2/3 =

(1/27 × 3/2) + 2/3 =

(1/18) + 2/3 =

1/18 + 12/18 =

13/18

A resposta é 13/18