SOLUTION: Represent each repeating decimal as the quotient of two intergers. _ 0.5 =0.5555 Thank you, Michelle

Represent each repeating decimal as the quotient of two intergers. 
  _
0.5 =0.5555 
Thank you, Michelle


Let 

(1)       N = 0.5555···

and label that "equation (1)"
Multiply both sides of equation (1) by 10

(2)     10N = 5.5555···

Now multiply both sides of equation (1) by -1

(3)      -N = -0.5555···

Now write equation (3) underneath equation (2),
draw a line and subtract:

(2)     10N =  5.5555···
(3)      -N = -0.5555···
      -------------------
         9N =  5   (Note how the repeating decimals cancel out)

          N = 5/9

That's the answer, 5/9

Edwin

x = 0.55555555

10x = 5.555555555

10x-x = 5.55555555-0.5555555

9x = 5

x =