Question

помогите два задания сделать даю 15 баллов

Answer 1

1
0,(6)=(6,6-0,6)/9=2/3
0,1(6)=(16,6-1,6)/90=15/90=1/6
2*2/3-1/6=4/3-1/6=8/6-1/6=7/6
2
0,(5)=(5,5-0,5)/9=5/9
0,8(3)=(83,3-8,3)/90=75/90=5/6
1+5/6=1 5/6
5/9:1 5/6=5/9*6/11=10/33

Answer 2

$1)\; \; a=0,(6)\\\\10a=6,(6)\; \; \to \\\\10a-a=6,(6)-0,(6)\\\\9a=6\; \; \to \; \; \; a=\frac{6}{9}= \frac{2}{3}\\\\b=0,1(6)\; ,\; \; 10b=1,(6)\; ,\; \; 100b=16,(6)\\\\100b-10b=90b=15\; \; \to \; \; b=\frac{15}{90}=\frac{1}{6}\\\\\\2\cdot 0,(6)-0,1(6)=2\cdot \frac{2}{3} -\frac{1}{6}= \frac{8-1}{6}= \frac{7}{6}$

$2)\; \; a=0,(5)\; ,\; \; 10a=5,(5)\\\\10a-a=9a=5\; \; \to \; \; a=\frac{5}{9} \\\\b=0,8(3)\; \; ,\; \; 10b=8,(3)\; \; ,\; \; 100b=83,(3)\\\\100b-10b=90b=75\; \; \to \; \; b= \frac{75}{90}= \frac{5}{6}\\\\\\ \frac{0,(5)}{1+0,8(3)} = \frac{\frac{5}{9}}{1+\frac{5}{6}} = \frac{5\cdot 6}{9\cdot 11} = \frac{10}{33}$