Question

Obtenha as geratrizes das seguintes dízimas periódicas:
a)0,777...
b)2,333...
c)0,151515...
d)3,12
e)4,7222...
f)0,527

Answer 1

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

b)2,333
x=2,333.(10)
10x=23,333
-  x=  2,333
 9x= 21
  x= 21/9

c)0,151515
x=0,151515.(100)
100x=15,151515
-    x=  0,151515
 99x=15
     x= 15/99

d)3,12
x=3,12.(10)
10x=31,12
-  x=  3,12
 9x=28
   x=28/9

e)4,7222
x=4,7222.(100)
100x=472,7222
-    x=     4,7222
 99x= 468
     x= 468/99

f)0,527
x=0,527.(10)
10x=5,527.(100)
1000x=527,527
-   10x=   5,527
  990x= 522
        x= 522/990