Chapter 4.2, Problem 43IP

a.

To determine

To write : the number using a negative exponent

Answer to Problem 43IP

The negative exponent of the number $\frac{1}{10000}$ is ${10}^{-4}$

Explanation of Solution

Given information :

A grain of sand has a volume of about $\frac{1}{10000}$ cubic millimeter

Calculation :

Therefore, the negative exponent of the number is

  $\begin{array}{l}\frac{1}{10000}\\ =\frac{1}{{10}^4}\\ ={10}^{-4}\end{array}$

The negative exponent is $-4$

Hence,thenegative exponent of the number $\frac{1}{10000}$ is ${10}^{-4}$

b.

To determine

To find : what is the approximate volume of the sand art bottle

Answer to Problem 43IP

The approximate is ${10}^6\text{ cubic millimeter }$ volume of the sand art bottle

Explanation of Solution

Given information :

A grain of sand has a volume of about $\frac{1}{10000}$ cubic millimeter

An empty bottle used to create sand art can hold about ${10}^{10}$ grains of sand

Calculation :

The volume of the grains of sand is $\frac{1}{10000}$ cubic millimeter and the number of grains of sand is ${10}^{10}$

  $\begin{array}{l}{10}^{10}\cdot {10}^{-4}\\ ={10}^{10+\left(-4\right)}\\ ={10}^{10-4}\\ ={10}^6\text{ cubic millimeter }\end{array}$

Hence, the approximate is ${10}^6\text{ cubic millimeter }$ volume of the sand art bottle.

c.

To determine

To find : how many cubic centimeter of sand will the bottle hold

Answer to Problem 43IP

The bottle will hold ${10}^3{\text{cm}}^3$ of sand.

Explanation of Solution

Given information :

A grain of sand has a volume of about $\frac{1}{10000}$ cubic millimeter

One cubic centimeter is equal to ${10}^3$ cubic millimeter.

Calculation :

  $\begin{array}{l}1{\text{ cm}}^3={10}^3{\text{mm}}^3\\ {10}^6{\text{mm}}^3\cdot \frac{1{\text{ cm}}^3}{{10}^3{\text{mm}}^3}\\ ={10}^{6-3}\cdot 1{\text{ cm}}^3\\ ={10}^3\cdot 1{\text{ cm}}^3\\ ={10}^3{\text{cm}}^3\end{array}$ .

Hence, the bottle will hold ${10}^3{\text{cm}}^3$ of sand.