Bài 1:
\({2 \over {125}} = 0,016;\,\,\,{3 \over {11}} = 0,\left( {27} \right).\)
Bài 2:
\(0,324\left( {1345} \right) = {{3241345 - 324} \over {9999000}} = {{3241021} \over {9999000}}.\)
Bài 3:
a) Ta có: \(0,\left( {13} \right) = {{13} \over {99}};\,\,\,\,1,\left( {86} \right) = {{185} \over {99}}\).
Vậy
\(0,\left( {13} \right) + 1,\left( {86} \right) - {5 \over 7} \)
\(= {{13} \over {99}} + 1 + {{86} \over {99}} - {5 \over 7}\)
\( = {{13} \over {99}} + {{86} \over {99}} + 1 - {5 \over 7} \)
\(= 1 + 1 - {5 \over 7} = {9 \over 7}.\)
b) Ta có \(0,(4) = {4 \over 9}.\)
Vậy
\({\left[ {0,\left( 4 \right)} \right]^2} - {1 \over {81}} + {{22} \over {27}} \)
\(= {{16} \over {81}} - {1 \over {81}} + {{22} \over {27}} = 1.\)
Bài 4: Ta có:
\(1,\left( {23} \right) = 1 + {{23} \over {99}} = {{122} \over {99}};\)
\(0,\left( {27} \right) = {{27} \over {99}} = {3 \over {11.}}\)
Vậy \(\left| {{{122} \over {99}} - x} \right| = {3 \over {11}}\)
\(\Rightarrow {{122} \over {99}} - x = {3 \over {11}}\) hoặc \({{122} \over {99}} - x = - {3 \over {11}} \)
\(\Rightarrow x = {{95} \over {99}}\) hoặc \(x = {{149} \over {99}}.\)
