Chapter 3, Problem 94A

Interpretation Introduction

Interpretation : The density in units of ${\text{kg/dm}}^3$ is to be expressed.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 94A

The density in units of ${\text{kg/dm}}^3$ is $5.52{\text{kg/dm}}^3$ .

Explanation of Solution

Given information :

The density of earth is $5.52{\text{g/cm}}^3$ .

It is known that $1\text{kg}={10}^3\text{g}$ and $1{\text{dm}}^3={10}^3{\text{cm}}^3$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is ${\text{g/cm}}^3\to {\text{kg/dm}}^3$ .

The conversion of the value is given as

  $\begin{array}{c}5.52{\text{g/cm}}^3\text{= }\frac{5.52\cancel{\text{g}}}{\cancel{{\text{cm}}^3}}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\times \frac{1\cancel{{\text{cm}}^3}}{{10}^{-3}{\text{dm}}^3}\left(\because 1\text{kg}={10}^3\text{g},1{\text{dm}}^3={10}^3{\text{cm}}^3\right)\\ =5.52{\text{kg/dm}}^3\end{array}$

Conclusion

The density in units of ${\text{kg/dm}}^3$ is $5.52{\text{kg/dm}}^3$ .