The reaction is:
#Fe_2O_3(s)+3CO(g)->2Fe(s)+3CO_2(g)#
Since #CO# is used in excess, therefore, the limiting reactant is #Fe_2O_3#.
#?g Fe(s) = underbrace(1.00xx10^3cancel(gFe_2O_3)xx(1cancel(molFe_2O_3))/(160 cancel(gFe_2O_3)))_(color(blue)("From g to mol"))xxunderbrace((2cancel(molFe))/(1cancel(molFe_2O_3)))_(color(blue)("Molar Ratio"))xxunderbrace((55.9gFe)/(1cancel(molFe)))_(color(blue)("From mol to g"))=color(green)(699gFe)#
I used 3 significant figures since #1.00kg# is 3 significant figures.
Explaining the dimensional analysis used above:
The first part:
#1.00xx10^3cancel(gFe_2O_3)xx(1cancel(molFe_2O_3))/(160 cancel(gFe_2O_3))#
is used to convert #gFe_2O_3# to #molFe_2O_3#
The second part:
#(2cancel(molFe))/(1cancel(molFe_2O_3))#
is the molar ration between #Fe# and #Fe_2O_3#. This is taking from the coefficient of the balanced equation.
The third part:
#(55.9gFe)/(1cancel(molFe))#
is used to convert #molFe# to #gFe#.
