Question

qual a fração geratriz de 1,1414141414...

2,1414141414...

0,43333....

0,53222....

2,87111.....

0,61888....

2,61111....

2,83737...

4,842222.....

2,94333....

5,531111....

0,83535....

1,43333.....​

Answer 1

A) 1,14141414141414....

x= 1,14141414...

100x=114,141414...

• 100x= 114,1414141414...
• -x= 1,14141414...
• 99x= 113
• x= 113/99

B) 2,1414141414...

x= 2,1414141414...

100x= 214,14141414...

• 100x= 214,14141414...
• -x= 2,141414141414...
• 99x= 212
• x= 212/99

C)

x= 0,433333...

10x= 4,33333...

100x= 43,3333...

• 100x= 43,3333...
• -10x= 4,33333...
• 90x= 39
• x= 39/90

D)

x= 0,532222...

100x= 53,2222...

1000x= 532,2222...

• 1000x= 532,2222...
• -100x= 53,22222....
• 900x= 479
• x= 479/900

E)

x= 2,87111111...

100x= 287,111111...

1000x= 2871,11111...

• 1000x= 2871,11111....
• -100x= 287,111111...
• 900x= 2584
• x= 2584/900

F)

x= 0,618888...

100x= 61,8888...

1000x= 618,8888...

• 1000x= 618,8888...
• -100x= 61,8888...
• 900x= 557
• x= 557/900

G)

x= 2,61111....

10x= 26,1111...

100x= 261,11111...

• 100x= 261,1111...
• -10x= 26,1111...
• 90x= 235
• x= 235/90

H)

x= 2,8373737...

10x= 28,373737...

1000x= 2837,373737...

• 1000x= 2837,3737373...
• -10x= 28,373737...
• 990x= 2809
• x= 2809/990

I)

x= 4,842222...

100x= 484,2222...

1000x= 4842,22222...

• 1000x= 4842,22222...
• -100x= 484,22222....
• 900x= 4358
• x= 4358/900

J)

x= 2,9433333...

100x=294,3333...

1000x= 2943,3333...

• 1000x= 2943,3333...
• -100x= 294,33333...
• 900x= 2649
• x= 2649/900

K)

x= 5,531111...

100x= 553,111111...

1000x= 5531,1111...

• 1000x= 5531,11111...
• -100x= 553,111111...
• 900x= 4978
• x= 4978/900

L)

x= 0,8353535...

10x= 8,35353535...

1000x= 835,353535...

• 1000x= 835,35353535...
• -10x= 8,353535...
• 990x= 827
• x= 827/990

M)

x= 1,43333...

10x= 14,3333...

100x= 143,333...

• 100x= 143,333...
• -10x= 14,33333...
• 90x= 129/90