Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as \(X \times 10^3 kg m ^{-3}\), where the value of \(X\) is :

(D) 7.7
Mass of the metallic cube, m=5.580 kg (4 significant figures)
Side length of the cube, \(a = 9 . 0 ~ c m = 9 . 0 \times 1 0 ^{- 2 } m\) (2 significant figures)
Volume of the cube, \(V=a^3=\left(9.0 \times 10^{-2}\right)^3=729 \times 10^{-6} m^3\)
Density of the material, \(\rho=\frac{m}{V}=\frac{5.580}{729 \times 10^{-6}}=7.6543 \ldots \times 10^3 kg m ^{-3}\)
In multiplication or division, the final result should retain as many significant figures as are present in the original number with the least significant figures. Here, the side length (9.0 cm) has the least number of significant figures, which is 2.
Rounding off \(7.6543 \ldots \times 10^3\) to 2 significant figures, we look at the third digit. Since the third digit is 5 and is followed by nonzero digits, the preceding digit is increased by 1 .
\(\rho=7.7 \times 10^3 kg m ^{-3}\)
Comparing this with \(X \times 10^3 kg m ^{-3}\), we get \(X=7.7\).