Chapter 1, Problem 1.52AP

Which quantity in each pair is larger?

1. a. 10 km or 10 m
2. b. 10 L or 10 mL
3. c. 10 g or 10 μg
4. d. 10 cm or 10 mm

Interpretation Introduction

Interpretation:

The larger quantity $\left(\text{10}\text{km}\left(\text{or}\right)\text{10}\text{m}\right)$ has to be determined.

Concept Introduction:

Important features of the metric system:

1. 1) Each kind of measurement has a base unit.
2. 2) All other units are connected to the base unit by powers of 10.
3. 3) The prefix of the unit name decides if the unit is larger or smaller than the base unit.

Answer to Problem 1.52AP

The larger quantity is $\text{10}\text{km}\text{.}$

Explanation of Solution

The expansion of $\text{10}\text{km}$ is 10kilometers.  The expansion of $\text{10}\text{m}$ is 10meters.

Meters is converted into kilometers as,

  $\frac{\text{1}\text{km}}{\text{1000}\text{m}}$

The value $\text{10}\text{m}$ is converted as,

  $\begin{array}{l}\text{km=10}\cancel{\text{m}}\text{×}\frac{\text{1}\text{km}}{\text{1000}\cancel{\text{m}}}\\ \text{km=0}\text{.01}\text{km}\end{array}$

The larger quantity is $\text{10}\text{km}$ because $\text{10}\text{m}$ expressed in kilometers is $\text{0}\text{.01}\text{km,}$ which is smaller.

Interpretation Introduction

Interpretation:

The larger quantity $\left(\text{10}\text{L}\left(\text{or}\right)\text{10 mL}\right)$ has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.52AP

The larger quantity is $\text{10}\text{L}\text{.}$

Explanation of Solution

The expansion of $\text{10}\text{L}$ is $\text{10}$ Liters.  The expansion of $\text{10}\text{mL}$ is $10$ milliliters.

Milliliters is converted to Liters as,

  $\frac{\text{1}\text{L}}{\text{1000}\text{mL}}$

The value $\text{10}\text{mL}$ is converted as,

  $\begin{array}{l}\text{L=10}\cancel{\text{mL}}\text{×}\frac{\text{1}\text{L}}{\text{1000}\cancel{\text{mL}}}\\ \text{L=0}\text{.01}\text{L}\end{array}$

The larger quantity is $\text{10}\text{L}$ because $\text{10}\text{mL}$ expressed in liters is $\text{0}\text{.01}\text{L,}$ which is smaller.

Interpretation Introduction

Interpretation:

The larger quantity $\left(\text{10}\text{g}\left(\text{or}\right)\text{10}\text{μg}\right)$ has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.52AP

The larger quantity is $\text{10}\text{g}\text{.}$

Explanation of Solution

The expansion for $\text{10}\text{g}$ is $\text{10}$ grams.  The expansion of $\text{10}\text{μg}$ is $\text{10}$ micrograms.

Micrograms is converted to grams as,

  $\frac{\text{1}\text{g}}{{\text{10}}^{\text{6}}\text{μg}}$

The value $\text{10}\text{μg}$ is converted into grams as,

  $\begin{array}{l}\text{g=10}\cancel{\text{μg}}\text{×}\frac{\text{1}\text{g}}{{\text{10}}^{\text{6}}\cancel{\text{μg}}}\\ \text{g=0}\text{.00001}\text{g}\end{array}$

The larger quantity is $\text{10}\text{g}$ because $\text{10}\text{μg}$ expressed in grams is $\text{0}\text{.00001}\text{g,}$ which is smaller.

Interpretation Introduction

Interpretation:

The larger quantity $\left(\text{10}\text{cm}\left(\text{or}\right)\text{10}\text{mm}\right)$ has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 1.52AP

The larger quantity is $\text{10}\text{cm}\text{.}$

Explanation of Solution

The expansion of $\text{10}\text{cm}$ is $10$ centimeter.  The expansion of $\text{10}\text{mm}$ is $\text{10}$ millimeter.

Millimeter is converted into centimeter as,

  $\frac{\text{1}\text{cm}}{\text{10}\text{mm}}$

The value $\text{10}\text{mm}$ is converted as,

  $\begin{array}{l}\text{cm=10}\cancel{\text{mm}}\text{×}\frac{\text{1}\text{cm}}{\text{10}\cancel{\text{mm}}}\\ \text{cm=1}\text{cm}\end{array}$

The larger quantity is $\text{10}\text{cm}$ because $\text{10}\text{mm}$ expressed in meters is $\text{1}\text{cm,}$ which is smaller.