Bài 1 :
a) Ta có : \(0,\left( 9 \right) = {9 \over 9} = 1\)
\(\Rightarrow 1 - 0,\left( 9 \right) + {5 \over 3} = 1 - 1 + {5 \over 3} = {5 \over 3}\)
b) \(0,\left( 2 \right) + 0,\left( 8 \right) = {2 \over 9} + {8 \over 9} = {{10} \over 9}.\)
Bài 2:
\(2,12\left( {345} \right) = 2 + {{12345 - 12} \over {99900}} = 2 + {{4111} \over {33300}} \)\(\;= {{70711} \over {33300}}.\)
Bài 3:
\({1 \over 8} = 0,125;\,\,\,{{20} \over 7} = 2,\left( {857142} \right).\)
Bài 4: Ta có: \(0,\left( 1 \right) = 0,125;\,\,\,1,\left( 9 \right) = 1 + {9 \over 9} = 2\)
Vậy \(\left| {x - 0,\left( 1 \right)} \right| = 1,\left( 9 \right)\) hay là \(\left| {x - {1 \over 9}} \right| = 2\)
\( \Rightarrow x - {1 \over 9} = 2\) hoặc \(x - {1 \over 9} = - 2 \)
\(\Rightarrow x = {{19} \over 9}\) hoặc \(x = - {{17} \over 9}.\)
