Question

Determine a fração geratriz das dízimas abaixo: (simples e compostas)
a) 0,171717...
b) 0,231231231...
c) 1,454545...
d) 2,13421342....
e) 0,99999....
f) 0,855555...
g) 0,9777777....
h) 0,61343434....
i) 1,544444...
j) 2,8232323....

Answer 1

Resposta:

Explicação passo-a-passo:

a)

$x=0,1717...\\100x=17,17...\\\\\frac{17}{99}$

b)

$x=0,231...\\1000x=231,231...\\\\\frac{231}{999}$

c)

$x=1,45...\\100x=145,45...\\\\\frac{144}{99}$

d)

$x=2,1342...\\10000x=2 1\:342,1342...\\\\\frac{21\:340}{9\:999}$

e)

$x=0,999...\\10x=9,999...\\\\\frac{9}{9}$

Tecnicamente essa fração geratriz não existe.

Os símbolos 0,999... e 1 representam a mesma ideia.

f)

$x=0,8555....\\100x=85,555...\\10x=8,555...\\\\\frac{77}{90}$

g)

$x=0,9777...\\100x=97,777...\\10x=9,777....\\\\\frac{88}{90}$

h)

$x=0,61343434...\\10000x=6\:134,343434...\\100x=61,343434...\\\\\frac{6073}{9900}$

i)

$x=1,5444...\\100x=154,444...\\10x=15,444...\\\\\frac{139}{90}$

j)

$x=2,8232323...\\1000x=2\:823,232323...\\10x=28,232323...\\\\\frac{2\:795}{990}$

Espero ter ajudado!

Desculpe qualquer erro.