Chapter 3, Problem 76A

Interpretation Introduction

Interpretation : The number of milliliters is to be calculated.

Concept Introduction : Dimensional analysis is a useful method for resolving conversion issues where measurements in one unit are changed to equal measurements in another.

Answer to Problem 76A

The number of milliliters is ${10}^6\text{mL}$ .

Explanation of Solution

Given information :

The given value is $\text{1}{\text{m}}^3$ .

It is known that $1{\text{m}}^3={10}^6{\text{cm}}^3$ , $1\text{L}={10}^3{\text{cm}}^3$ and $1\text{L}={10}^3\text{mL}$ .

The desired conversion is ${\text{m}}^3\to \text{mL}$ .

The conversion of the value is given as

  $\begin{array}{c}1{\text{m}}^3\text{=}1\cancel{{\text{m}}^3}\times \frac{{10}^6\cancel{{\text{cm}}^3}}{1\cancel{{\text{m}}^3}}\times \frac{{10}^{-3}\cancel{\text{L}}}{1\cancel{{\text{cm}}^3}}\times \frac{{10}^3\text{mL}}{1\cancel{\text{L}}}\left(\because 1{\text{m}}^3={10}^6{\text{cm}}^3,1\text{L}={10}^3{\text{cm}}^3,1\text{L}={10}^3\text{mL}\right)\\ ={10}^6\text{mL}\end{array}$

Conclusion

The number of milliliters is ${10}^6\text{mL}$ .