We get in trouble with your question, because you used "simplify" 
verb...which should have been refering to other SAGE simplifying functions 
(floor, simplify symbolic expression and so on).... when you wanted to 
"display only few significant digits of that real number".

Function for you is :  n(digits=...)

Try this in cell to understand better :

m = 12.0000000 ; print m
print type(m)
mr = m.n(digits=3) ; print mr
print type(mr)
x = m - mr + 1; print x
print type(x)
y = x.n(digits=5) ; print y
print type(y)
z = y ; print z
print type(z)
u = 1.000
ur = u.n(digits=8) ; print ur
print "n() is attribute of object RealNumber :"
print z
print ur

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