[tex]x=2\frac{3}{9}-[(-\frac{2}{3})^{-2}]^{1002}\cdot(-\frac{4}{9}^{1001}=\\
2\frac{1}{3}-[(-\frac{3}{2})^2]^{1002}\cdot (-\frac{4}{9})^{1001}=\\
2\frac{1}{3}-(\frac{9}{4})^{1002}\cdot(-\frac{4}{9})^{1001}=\\
2\frac{1}{3}+(\frac{9}{4})^{1002}\cdot(\frac{4}{9})^{1001}=\\
2\frac{1}{3}+\frac{9}{4}\cdot(\frac{9}{4}\cdot\frac{4}{9})^{1001}=\\
2\frac{1}{3}+\frac{9}{4}=2^{4)}\frac{1}{3}+2^{3)}\frac{1}{4}=4\frac{7}{12}\\
\{x\}=\frac{7}{12}=0,58(3)
[/tex]
