ГДЗ по алгебре и начала математического анализа 11 класс Алимов Задание 93

\[\boxed{\mathbf{93}\mathbf{.}}\]

\[1)\ Дробь\ 1,3(1).\]

\[Пусть\ x - данная\ дробь,\ тогда:\]

\[x = 1,3(1);\]

\[10x = 13,(1);\]

\[100x = 131,(1);\]

\[x = \frac{90x}{90} = \frac{100x - 10x}{90} =\]

\[= \frac{131,(1) - 13,(1)}{90} = \frac{118}{90} =\]

\[= \frac{59}{45} = 1\frac{14}{45}.\]

\[Ответ:\ \ 1\frac{14}{45}.\]

\[2)\ Дробь\ 2,3(2).\]

\[Пусть\ x - данная\ дробь,\ тогда:\]

\[x = 2,3(2);\]

\[10x = 23,(2);\]

\[100x = 232,(2);\]

\[x = \frac{90x}{90} = \frac{100x - 10x}{90} =\]

\[= \frac{232,(2) - 23,(2)}{90} = \frac{209}{90} =\]

\[= 2\frac{29}{90}.\]

\[Ответ:\ \ 2\frac{29}{90}.\]

\[3)\ Дробь\ 0,(248).\]

\[Пусть\ x - данная\ дробь,\ тогда:\]

\[x = 0,(248);\]

\[1000x = 248,(248);\]

\[x = \frac{999x}{999} = \frac{1000x - x}{999} =\]

\[= \frac{248,(248) - 0,(248)}{999} = \frac{248}{999}.\]

\[Ответ:\ \ \frac{248}{999}.\]

\[4)\ Дробь\ 0,(34);\]

\[Пусть\ x - данная\ дробь,\ тогда:\]

\[x = 0,(34);\]

\[10x = 34,(34);\]

\[x = \frac{99x}{99} = \frac{100x - x}{99} =\]

\[= \frac{34,(34) - 0,(34)}{99} = \frac{34}{99}.\]

\[Ответ:\ \ \frac{34}{99}.\]