Question

2. Obtenha as geratrizes das seguintes d´ızimas peri´odicas: a) 0,666 . . . b) 0,121212 . . . c) 4,727272 . . . d) 1,8999 . . . e) 1,2616161 . . .

Answer 1

a)

a=0,666...

10a=6,6666...

10a-a=6

a=6/9=2/3

b)

a=0,1212....

100a=12,1212..

100a-a=12

a=12/99=4/33

c)

a=4,7272....

100a=472,7272...

100a-a=468

a=468/99

d)  observe >>>0,9999...=1    e 0,09999...=0,1

a=1,89999... =1,9

10a=18,9999...

100a=189,999...

100a-10a =171

a=171/90

e)

a=1,2616161....

10a=12,6161...

1000a=1261,6161...

1000a-10a =1249

a=1249/990