Solution

The iron oxide has 69.9% iron and 30.1% dioxygen by mass.
Thus, 100 g of iron oxide contains 69.9 g iron and 30.1 g dioxygen.
The number of moles of iron present in 100 g of iron oxide are $$\displaystyle \frac {69.9}{55.8} = 1.25$$.
The number of moles of dioxygen present in 100 g of iron oxide are $$\displaystyle \frac {30.1}{32} = 0.94$$.
The ratio of the number of oxygen atoms to the number of carbon atoms present in one formula unit of iron oxide is
$$\displaystyle \frac {2 \times 0.94}{1.25} = 1.5:1=3:2$$.
Hence, the formula of the iron oxide is $$\displaystyle Fe_2O_3 $$.