0,(27) = 0,272727…
a = 0,(27)
100a = 27,(27)
100a - a = 27,(27) - 0,(27)
99a = 27
a=\frac{27}{99}
0,(9) = 0,999…
b = 0,(9)
10b = 9,(9)
10b - b = 9,(9) - 0,(9)
9b = 9
b=\frac{9}{9}=1
0,(405)=0,405405405…
c=0,(405)
1000c = 405,(405)
100b - b = 405,(405) - 0,(405)
999c = 405
c=\frac{405}{999}
{\frac{0,5-0,(27)}{0,(9)}+0,(405)*2\frac{7}{15}=\frac{\frac{1}{2}-\frac{27}{99}}{1}+\frac{\not405^{27}}{999}\cdot \frac{37}{\not15^1}=(\frac{99}{198}-\frac{54}{198})+\frac{27}{999}\cdot 37=}
=\frac{45}{198}+\frac{999}{999}=1\frac{45}{198}=1\frac{5}{22}