If you want to print only, say, 3 significant digits, you can do:
sage: B = random_matrix(RDF,5,5)
sage: B
[ 0.23432333232 -0.227616100926 -0.599156411098 0.41166189832 0.764641434688]
[ 0.439380654181 -0.320536940171 0.320947963409 -0.847122064875 0.404266447713]
[ -0.908186671809 0.622848454479 0.219215554761 -0.872284101116 -0.286278011806]
[ -0.68809928219 0.779797277388 0.12146772553 0.864262076944 -0.0156592746181]
[ 0.807522456479 -0.294491803547 -0.569575247674 -0.850921782049 -0.521678331812]
sage: print B.str(rep_mapping=lambda x : str(x.n(digits=3)))
[ 0.234 -0.228 -0.599 0.412 0.765]
[ 0.439 -0.321 0.321 -0.847 0.404]
[ -0.908 0.623 0.219 -0.872 -0.286]
[ -0.688 0.780 0.121 0.864 -0.0157]
[ 0.807 -0.294 -0.570 -0.851 -0.522]