Question

запишите в виде обыкновенных дробей: 2,(8); 5,1(12); 3,16(54;​

Answer 1

$1)\; \; a=2,(8)=2,888...\\\\10a=28,(8)\\\\10a-a=28,(8)-2,(8)\\\\9a=26\\\\a=\frac{26}{9}\\\\\\2)\; \; a=5,1(12)=5,1121212...\\\\10a=51,(12)\; \; ;\; \; \; 1000a=5112,(12)\\\\1000a-10a=5112,(12)-51,(12)\\\\990a=5061\\\\a=\frac{5061}{990}=\frac{1687}{330}$

$3)\; \; a=3,16(54)=3,16545454...\\\\100a=316,(54)\\\\10000a=31654,(54)\\\\10000a-100a=31654.(54)-316,(54)\\\\9900a=31338\\\\a=\frac{31338}{9900}=\frac{1741}{550}$