Chapter 3.3, Problem 49SP

Interpretation Introduction

Interpretation : The number of red blood cells is to be calculated.

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 49SP

The number of red blood cells is $7.0\times {10}^{12}\text{RCBs/L}$ .

Explanation of Solution

Given information :

The count of red blood cells in the blood of $1.0{\text{mm}}^3$ is $7\times {10}^6$ .

The volume of blood is $1.0{\text{mm}}^3$ .

It is known that $\text{1}{\text{m}}^3\text{=}{\text{10}}^9{\text{mm}}^3$ , $\text{1}{\text{m}}^{\text{3}}\text{=}{\text{10}}^{\text{3}}{\text{dm}}^{\text{3}}$ and $\text{1}\text{L}\text{=}\text{1}{\text{dm}}^3$ .

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 count of red blood cells in the blood of $1.0{\text{mm}}^3$ is given as $\frac{7\times {10}^6}{1.0{\text{mm}}^3}$ .

The count of red blood cells in the blood of $1.0\text{L}$ is given as

  $\begin{array}{c}\frac{\text{RBC}}{1\text{L}}=\left(\frac{7\times {10}^6\text{RBC}}{1.0{\text{mm}}^3}\right)\left(\frac{{10}^9{\text{mm}}^3}{1{\text{m}}^3}\right)\left(\frac{1{\text{m}}^3}{{10}^3{\text{dm}}^3}\right)\left(\frac{1{\text{dm}}^3}{1\text{L}}\right)\left(\begin{array}{l}\because \text{1}{\text{m}}^3\text{=}{\text{10}}^9{\text{mm}}^3,\text{1}{\text{m}}^{\text{3}}\text{=}{\text{10}}^{\text{3}}{\text{dm}}^{\text{3}},\\ \text{1}\text{L}\text{=}\text{1}{\text{dm}}^3\end{array}\right)\\ =7.0\times {10}^{12}\text{RCBs/L}\end{array}$

Conclusion

The number of red blood cells is $7.0\times {10}^{12}\text{RCBs/L}$ .