Chapter 1, Problem 1.59PAE

1.55 Convert 22.3 mL to (a) liters, (b) cubic inches, and (c) quarts.

Interpretation Introduction

To convert:

$22.3mL$to (liter) $L$.

Explanation of Solution

The first step in unit conversion is to identify the prefixes involved. Then relate them to the base unit.

Note that base unit of volume is “Liter”.

Prefixes involved “milli” which stands for $\text{1}{0}^{-\text{3}}$

Solve$\left(22.3mL\right)\times \left(\frac{1L}{1000mL}\right)=2.23\times {10}^{-2}L$

Interpretation Introduction

To convert:

$22.3mL$to cubic inches.

Explanation of Solution

The first step in unit conversion is to identify the prefixes involved. Then relate them to the base unit.

Note that base unit of volume is “Liter”.

Prefixes involved “milli” which stands for $\text{1}{0}^{-\text{3}}$

Note that the required amount if cubic inch. Length can be related to volume via the third power. Therefore, we must relate Liter to length first.$1L=1000c{m}^3$

Conversion factors required:$\begin{array}{l}1000mL=1000c{m}^3\\ 1in=2.54cm\end{array}$

Convert

$\begin{array}{l}\left(22.3mL\right)\times \left(\frac{1000c{m}^3}{1000mL}\right)=22.3c{m}^3\\ \left(22.3c{m}^3\right)\times {\left(\frac{1in}{2.54cm}\right)}^3=1.36082i{n}^3\\ V=1.36i{n}^3\end{array}$

Interpretation Introduction

To convert:

$22.3mL$to quarts.

Explanation of Solution

The first step in unit conversion is to identify the prefixes involved. Then relate them to the base unit.

Note that base unit of volume is “Liter”.

Prefixes involved “milli” which stands for 10-3

Note that the required amount if cubic inch. Length can be related to volume via the third power. Therefore, we must relate Liter to length first.$1L=1000c{m}^3$

Conversion factors required:$\begin{array}{l}1000mL=1000c{m}^3\\ 1in=2.54cm\\ 1qt=\text{57}\text{.75}i{n}^3\end{array}$

Convert$22.3mL=$

$\begin{array}{l}\left(22.3mL\right)\times \left(\frac{1000c{m}^3}{1000mL}\right)=22.3c{m}^3\\ \left(22.3c{m}^3\right)\times {\left(\frac{1in}{2.54cm}\right)}^3=1.36082i{n}^3\\ (1.36i{n}^3)\times \left(\frac{1qt}{\text{57}\text{.75}i{n}^3}\right)=\text{0}\text{.02356}qt\\ \text{0}\text{.02356}qt\end{array}$

Conclusion

When converting units in the same system, it is imperative to assign the correct value to the prefixes. When using conversion factors with non-exact values, use significant figures to keep the uncertainty.