Question

calcule a geratriz de cada dizima

a)0,7777...
b)2,535353...
c)1,238238238...
d)0,2353535...

Answer 1

A) 0,777...


x = 0,777...

10x = 7,777...

10x = 7 + x

10x - x = 7 + x - x

9x = 7

9x/9 = 7/9

x = 7/9


B) 2,5353...


x = 2,5353...(A)

100x = 253,5353...(B)

Fazendo B - A, temos:

100x - x = 253,5353... - 2,5353...

99x = 251

99x/99 = 251/99

x = 251/99


C) 1,238238...


x = 1,238238...(A)

1000x = 1238,238238... (B)

Fazendo B - A, temos:

1000x - x= 1238,238238... - 1,238238...

999x = 1237

999x/999 = 1237/999

x = 1237/999


D) 0,23535...


x = 0,23535...

10x = 2,3535...(A)

100x = 235,3535...(B)

Fazendo B - A, temos :

100x-10x = 235,3535... - 2,3535...

990x = 233

990x/990 = 233/990

x= 233/990