The repeating decimal, is converted to the fraction
What is the value of x in the fraction?


Hello!
By using a certain formula, a repeating number with two repeating digits will always become the number out of 99. In our case, we would get [tex] \frac{27}{99} [/tex].
To get the numerator to equal three, we divide both sides by 9.
[tex] \frac{27}{99} =\frac{3}{11} [/tex]
Therefore, x=11.
I hope this helps!
y = 0.272727...
100y = 27.2727...
- y = 0.2727...
-------------------------
99y = 27
y = 27/99
y = (3 * 9)/(11 * 9)
y = 3/11
0.272727... = 3/11 = 3/x
x = 11