Chapter 1, Problem 34P

Which quantity in each pair is larger?

1. 10 km or 10 m
2. 10 L or 10 mL
3. 10 g or 10 $\text{μg}$
4. 10 cm or 10 mm

Interpretation Introduction

(a)

Interpretation:

The larger quantity between 10 km or 10 m needs to be determined.

Concept Introduction:

Unit's conversion is the conversion between different measurement units having the same quantity usually by multiplicative conversion factors. For example:

Quantity	Name of unit	Symbol	Value
length	millimeter centimeter meter kilometer	mm cm m km	10 mm = 1cm 100 cm = 1m 1000 m = 1km
mass	milligram gram kilogram tonne	mg g kg t	1000 mg = 1g 1000 g = 1kg 1000 kg = 1t

Answer to Problem 34P

10 km.

Explanation of Solution

To determine which is larger between 10 km or 10 m, convert 10 km into m using 1 km = 1000 m

Below conversion factor is used:

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

  $\text{10 km = 10 km}\times \frac{\text{1000 m}}{1\text{ km}}=10000\text{ m}$

Now, 10000 m is greater than 10 m. Therefore, 10 km is larger than 10 m.

Interpretation Introduction

(b)

Interpretation:

The larger quantity between 10 L or 10 mL needs to be determined.

Concept Introduction:

Unit's conversion is the conversion between different measurement units having the same quantity usually by multiplicative conversion factors. For e.g.

Quantity	Name of unit	Symbol	Value
length	millimeter centimeter meter kilometer	mm cm m km	10 mm = 1cm 100 cm = 1m 1000 m = 1km
mass	milligram gram kilogram tonne	mg g kg t	1000 mg = 1g 1000 g = 1kg 1000 kg = 1t

Answer to Problem 34P

10 L.

Explanation of Solution

To determine which is larger between 10 L or 10 mL, convert 10 L into mL using 1 L = 1000 mL

Below conversion factor is used:

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

  $\text{10 L = 10 L}\times \frac{\text{1000 mL}}{1\text{ L}}=10000\text{ mL}$

Now, 10000 mL is greater than 10 mL. Therefore, 10 L is larger than 10 mL.

Interpretation Introduction

(c)

Interpretation:

The larger quantity 10 g or 10 μg needs to be determined.

Concept Introduction:

Unit's conversion is the conversion between different measurement units having the same quantity usually by multiplicative conversion factors. For example:

Quantity	Name of unit	Symbol	Value
length	millimeter centimeter meter kilometer	mm cm m km	10 mm = 1cm 100 cm = 1m 1000 m = 1km
mass	milligram gram kilogram tonne	mg g kg t	1000 mg = 1g 1000 g = 1kg 1000 kg = 1t

Answer to Problem 34P

10 g.

Explanation of Solution

To determine which is larger between 10 g or 10 μg, convert 10 g into μg using 1 g = 1,000,000 μg

Below conversion factor is used:

  $\frac{1\text{ g}}{1,000,000\text{ µg}}\text{ or }\frac{1,000,000\text{ µg}}{1\text{ g}}$

  $\text{10 μg = 10 μg}\times \frac{\text{1 g}}{1,000,000\text{ μg}}=0.00001\text{ g}$

Now, 10 g is greater than 0.00001 g. Therefore, 10 g is larger than 10 $\text{μg}$.

Interpretation Introduction

(d)

Interpretation:

The larger quantity between 10 cm or 10 mm needs to be determined.

Concept Introduction:

Unit's conversion is the conversion between different measurement units having the same quantity usually by multiplicative conversion factors. For example:

Quantity	Name of unit	Symbol	Value
length	millimeter centimeter meter kilometer	mm cm m km	10 mm = 1cm 100 cm = 1m 1000 m = 1km
mass	milligram gram kilogram tonne	mg g kg t	1000 mg = 1g 1000 g = 1kg 1000 kg = 1t

Answer to Problem 34P

10 cm.

Explanation of Solution

To determine which is larger between 10 cm or 10 mm, convert 10 cm into m using 1 m = 100 cm

Below conversion factor is used:

  $\frac{1\text{ m}}{100\text{ cm}}\text{ or }\frac{100\text{ cm}}{1\text{ m}}$

  $\text{10 cm = 10 cm}\times \frac{\text{1 m}}{100\text{ cm}}=0.1\text{ m}$

Converting 10 mm into m using 1 m = 1000 mm

Below conversion factor is used:

  $\frac{1\text{ m}}{1000\text{ mm}}\text{ or }\frac{1000\text{ mm}}{1\text{ m}}$

  $\text{10 mm = 10 mm}\times \frac{\text{1 m}}{1000\text{ mm}}=0.01\text{ m}$

Now, 0.1 m is greater than 0.01 m. Therefore, 10 cm is larger than 10 mm.