Answer
d = 7.86 g / $cm^{3}$
Work Step by Step
d = 0.284 lb per 1 $in^{3}$
1 in = 2.54 cm
So 1 $in^{3}$ = 2.54 cm * 2.54 cm * 2.54 cm = 16.387064 $cm^{3}$
d = 0.284 lb per 16.387064 $cm^{3}$
1 kg = 2.205 lb
2.205 lb = 1 kg
2.205 lb = 1000 g
1 lb = 1000 / 2.205 g = 453.5147392 g
0.284 lb = 0.284 * 453.5147392 g = 128.7981859 g
d = 128.7981859 g per 16.387064 $cm^{3}$
d = 7.859747536 g per 1 $cm^{3}$
d = 7.859747536 g / $cm^{3}$
Rounding to 3 significant figures gives
d = 7.86 g / $cm^{3}$
