Question

qual a fraçao geratriz de a)0,777... b)0,444...c)0,18 d)2,333...e)1,5 f)2,35 g)0,02 h)1,235"

Answer 1

a) x = 0,777  10x = 7,777
10x - x = 7,77 - 0,77
9x = 7
x = 7/9

b) x = 0,444  10x = 4,444
10x - x = 4,44 - 0,44
9x = 4
x = 4/9

c) x = 0,18   100x = 18,18
100x - x = 18,18 - 0,18
99x = 18 
x = 18/99

d) x = 2,333  10x = 23,333
10x - x = 23,33 - 2,33
9x = 21
x = 21/9

e) x = 1,5     10x = 15,5
10x - x = 15,5 - 1,5
9x = 14
x = 14/9

f) x = 2,35    100x = 235,35
100x - x = 235,35 - 2,35
99x = 233
x = 233/99

g) x = 0,02    100x = 2,02
100x - x = 2,02 - 0,02
99x = 2
x = 2/99

h) x = 1,235    1000x = 1235,235
1000x - x = 1235,235 - 1,235
999x = 1234
x = 1234/999

Considerei que a letra f a dízima era 353535 ; na letra g 020202 e na letra h 235235235.

Answer 2

A) 0,777...
$x=0,777... (.10) \\ 10x= 7,777... \\ 10x=7 + x \\ 10x - x=7 \\9x=7\\x= \frac{7}{9}$

B) 0,444...
$x=0,444...(.10)\\10x=4,444...\\10x=4+x\\10x-x=4\\9x=4\\x= \frac{4}{9}$

C) 0,18
$0,18(.100)= \frac{18}{100}= \frac{9}{50}$

D) 2,333...
$x=2,333\\x=0,333...(.10)\\10x=3,333...\\10x=3+x\\10x-x=3\\9x=3\\x= \frac{3}{9}\\x= \frac{1}{3} \\2+ \frac{1}{3}= \frac{7}{3}$

E) 1,5
$1,5(.10) = \frac{15}{10}\\ \frac{15}{10} = \frac{3}{2}$

F) 2,35
$2,35(.100)= \frac{235}{100}= \frac{47}{20}$

G)0,02
$0,02(.100)= \frac{2}{100} = \frac{1}{50}$

H) 1,235
$1,235(.1000)= \frac{1235}{1000} = \frac{247}{200}$

Abraço! Segue o raciocínio que você aprende. É simples.