What is 5.57575757... as a fraction ?

Assuming you can't use a calculator:

5.575757... = 5 + 0.575757...

let 0.575757... = x

1) Substitute x for 0.575757...

5.575757... = 5 + x

2) Multiply both sides by 100

100(5.575757...) = 100(5+x)            

557.575757... = 500 + 100x    

3) Subtract 500 from both sides

57.575757... = 100x          

4) 57.575757... can be written as 57 + 0.575757...              

57 + 0.575757... = 100x

5) Substitute x for 0.575757...

57 + x = 100x

6) Subtract x from both sides

57 = 99x

7) divide both sides by 99

x = 57/99

8) plug in 57/99 for x in our original equation

5.575757... = 5 + (57/99)

9) simplify

5.575757... = ((5*99)/99) + (57/99)

5.575757... = (495/99) +(57/99)

5.575757... = (495+57)/99

5.575757... = 552/99

5.575757... as a fraction is 552/99

answer: need picture of problem

step-by-step explanation: