Question

9) Encontre a fração geratriz de cada dízima periódica a seguir:
passo a passo por favor

Answer 1

a)  0,3737... = 37


b) -0,8888... = -8/9


c)  0,5555... = 5/9


d) -3,2222... = -3 - 0,222.. = -3 - 2/9 = -27/9 - 2/9 = -29/9


e) -1,2121... = -1 - 0,2121... = -1 - 21/99 = -99/99 - 21/99 = -120/99 


f) 0,05050... = 50/990


g) 0,5656... = 56/99


h) 1,4343... = 1 + 0,4343... = 1 + 43/99 = 99/99 + 43/99 = 142/99


i ) 2,0101... =  2 + 0,01010... = 2 + 10/990 = 1980/990 + 10/990 = 1990/990 = 199/99

Answer 2

A) 0,373737

x= 0,373737... × 100
100x= 37,373737...
- x = 0,373737...
--------------------------------
99x= 37
x= 37/99

B)-0,888

x= -0,888... × 10
10x= -8,888...
- x = 0,888...
--------------------------------
9x= -8
x= -8/9

C) 0,555

x= 0,555... × 10
10x= 5,555...
- x = 0,555...
--------------------------------
9x=5
x= 5/9

D) -3,222

x= -3,222... × 10
10x= -32,222...
- x = 3,222...
--------------------------------
9x= -29
x= -29/9

E)-1,212121

x= -1,212121... × 100
100x= -121,212121...
- x = 1,212121...
--------------------------------
99x= -120
x= -120/99


F) 0,050505

x= 0,0505050... × 100
100x= 05,0505050...
- x = 0,0505050...
--------------------------------
99x= 5
x=5/99


G) 0,565656

x= 0,565656... × 100
100x= 56,565656...
- x = 0,565656...
--------------------------------
99x= 56
x= 56/99


H) 1,434343

x= 1,434343... × 100
100x= 143,434343...
- x = 1,434343...
--------------------------------
99x= 142
x= 142/99


I) 2,010101

x= 2,010101... × 100
100x=201,010...
- x = 2,010...
--------------------------------
99x= 199
x= 3
199/99