Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 510

\[\boxed{\mathbf{510}.}\]

\[1)\ Дробь\ 2,5(1);\]

\[Пусть\ x - данная\ дробь:\]

\[x = 2,5(1);\]

\[10x = 25,(1);\]

\[100x = 251,(1);\]

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

\[= \frac{251,(1) - 25,(1)}{90} =\]

\[= \frac{226}{90} = \frac{113}{45} = 2\frac{23}{45};\]

\[Ответ:\ \ 2\frac{23}{45}.\]

\[2)\ Дробь\ 1,3(2);\]

\[Пусть\ x - данная\ дробь:\]

\[x = 1,3(2);\]

\[10x = 13,(2);\]

\[100x = 132,(2);\]

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

\[= \frac{132,(2) - 13,(2)}{90} =\]

\[= \frac{119}{90} = 1\frac{29}{90};\]

\[Ответ:\ \ 1\frac{29}{90}.\]

\[3)\ Дробь\ 0,(248);\]

\[Пусть\ x - данная\ дробь:\]

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

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

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

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

\[Ответ:\ \ \frac{248}{999}.\]

\[4)\ Дробь\ 0,(35);\]

\[Пусть\ x - данная\ дробь:\]

\[x = 0,(35);\]

\[100x = 35,(35);\]

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

\[= \frac{35,(35) - 0,(35)}{99} = \frac{35}{99};\]

\[Ответ:\ \ \frac{35}{99}.\]