SOLUTION: I can’t figure this problem out. X=0.89 repeating decimal. 100x=89.89. 100x-x=89.89-? Sue began converting the repeating decimal 0.89 above to a fract

Algebra ->  Number-Line -> SOLUTION: I can’t figure this problem out. X=0.89 repeating decimal. 100x=89.89. 100x-x=89.89-? Sue began converting the repeating decimal 0.89 above to a fract      Log On


   

Question 1144329: I can’t figure this problem out. X=0.89 repeating decimal. 100x=89.89. 100x-x=89.89-?
Sue began converting the repeating decimal 0.89 above to a fraction so that she could use it during her calculations. Sue knew she had to set up equations, but as she began to solve it she was not sure of how to complete the problem. Help Sue solve the problem below by finding the fractional equivalent to the decimal 0.89 with a line over the 89.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

X = 0.8989...  is a repeating decimal.


100X = 89.8989...


100X = 89 + 0.8989...


100X = 89 +X


100X - X = 89


99X = 89


  X = 89%2F99 is the ratio you want to get.


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Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I can’t figure this problem out. X=0.89 repeating decimal. 100x=89.89. 100x-x=89.89-?
Sue began converting the repeating decimal 0.89 above to a fraction so that she could use it during her calculations. Sue knew she had to set up equations, but as she began to solve it she was not sure of how to complete the problem. Help Sue solve the problem below by finding the fractional equivalent to the decimal 0.89 with a line over the 89.
She had the following:

       x = 0.89 ------ eq (i)

    100x = 89.89 ----- eq (ii)

100x - x = 89.89 - 0.89 -------- Subtracting eq (i) from eq (ii)

     99x = 89

x, or fractional equivalent to 0.89 (overline): highlight_green%2889%2F99%29