a) $5.2\left(4\right)=5.2444444444444444\dots ..$

$5.24<5.2\left(4\right)$  

b) $6\frac{3}{5}=6.6$  

$6.\left(6\right)=6.66666666666\dots ..$

$6\frac{3}{5}<6.\left(6\right)$  

c) $3.\left(05\right)=3.05050505050505050505050505\dots ..$

$3.0\left(5\right)=3.05555555555\dots ..$

$3.\left(05\right)<3.0\left(5\right)$  

d) $0.0\left(123\right)=0.0123123123123123123\dots .$

$0.\left(123\right)=0.123123123123123123\dots .$

$0.0\left(123\right)<0.\left(123\right)$  

e) $12.\left(070\right)=12.070070070070070070\dots$

$12.0\left(70\right)=12.07070707070707070707070\dots$

$12.\left(070\right)<12.0\left(70\right)$  

f) $4.123=4.123123123123123123123\dots .$

$4.1\left(230\right)=4.1230230230230230\dots$

$4.\left(123\right)>4.1\left(230\right)$