Bài 1: \(\left[ {0,\left( 5 \right).0,\left( 2 \right)} \right]\,:\,\left( {3{1 \over 3}:{{33} \over {25}}} \right)\)\(\; - \left( {{2 \over 5}.1{1 \over 3}} \right):{4 \over 3}\)
\(\eqalign{ & = \left( {{5 \over 9}.{2 \over 9}} \right):\left( {{{10} \over 3}.{{25} \over {33}}} \right) - \left( {{2 \over 5}.{4 \over 3}} \right):{4 \over 3} \cr & = {{10} \over {81}}.{{99} \over {250}} - {2 \over 5} = {{11} \over {225}} - {2 \over 5} = {{ - 79} \over {225}} \cr} \)
Bài 2:
a) \(0,22\left( {23} \right) = 0,222323... > 0,2223.\)
b) \( - {1 \over 7} = - 0,142857142857...;\)
\( - 0.14285\left( {57} \right) = - 0,1428575757...\)
Ta thấy \(\eqalign{ & - 0,14285757 < - 0,142857142857 \cr & \Rightarrow - {1 \over 7} > - 0,1428\left( {57} \right). \cr} \)
Bài 3: Ta có : \(0,\left( 1 \right) = {1 \over 9} \)
\(\Rightarrow \left| {1 - x} \right| = \sqrt 2 - {1 \over 9} \)
\(\Rightarrow 1 - x = \sqrt 2 - {1 \over 9}\) hoặc \(1 - x = - \sqrt 2 + {1 \over 9} \)
\(\Rightarrow x = {{10} \over 9} - \sqrt 2 \) hoặc \(x = {8 \over 9} + \sqrt 2 \).
