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Numerical · Q21

Q.The density of a substance is 2.5×1032.5\times10^{3} kg m−3^{-3} in SI units. Express this density in CGS units (g cm−3^{-3}).

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2.5×103 kg m−3=2.5×103×1000 g(100 cm)32.5\times10^{3}\ \text{kg m}^{-3} = 2.5\times10^{3}\times\frac{1000\ \text{g}}{(100\ \text{cm})^{3}}

Since (100 cm)3=106 cm3(100\ \text{cm})^{3} = 10^{6}\ \text{cm}^{3}:

=2.5×103×1000106 g cm−3=2.5×103×10−3 g cm−3=2.5 g cm−3= 2.5\times10^{3}\times\frac{1000}{10^{6}}\ \text{g cm}^{-3} = 2.5\times10^{3}\times10^{-3}\ \text{g cm}^{-3} = 2.5\ \text{g cm}^{-3}

This confirms the well-known rule of thumb that a density in kg m−3^{-3} numerically becomes one-thousandth as large when re-expressed in g cm−3^{-3}.

[!ANSWER] 2.5×1032.5\times10^{3} kg m−3^{-3} is equal to 2.52.5 g cm−3^{-3}.

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