Chapter 5, Problem 96A

(a)

Interpretation Introduction

Interpretation: The given measurement $0.000039\text{kg}$ in scientific notation.

Concept introduction:

The number will be written as scientific notation when a number between 1 to10 is multiplied by a power of 10.

Answer to Problem 96A

  $3.9\text{1}\times {\text{10}}^{-2}\text{g}$

Explanation of Solution

  $\begin{array}{c}0.000039\text{kg}\text{= 3}\text{.9}\times {\text{10}}^{-5}\text{ kg}\\ \text{= 3}\text{.9}\times {\text{10}}^{-5}\times \text{1}\times {\text{10}}^3\text{g }\left(\because 1\text{kg}\text{= 1}\times {\text{10}}^3\text{g}\right)\\ =3.9\text{1}\times {\text{10}}^{-2}\text{g}\end{array}$

The $0.000039\text{kg}$ in scientific notion is $3.9\text{1}\times {\text{10}}^{-2}\text{g}$ .

(b)

Interpretation Introduction

Interpretation: The given measurement $\text{784 L}$ in scientific notation.

Concept introduction:

The number will be written as scientific notation when a number between 1 to10 is multiplied by a power of 10.

Answer to Problem 96A

  $\text{7}\text{.84}\times {\text{10}}^{-2}\text{ L}$

Explanation of Solution

  $\text{784 L = 7}\text{.84}\times {\text{10}}^{-2}\text{ L}$

The $\text{784 L}$ in scientific notion is $\text{7}\text{.84}\times {\text{10}}^{-2}\text{ L}$

(c)

Interpretation Introduction

Interpretation: The given measurement $0.0830\text{g}$ in scientific notation.

Concept introduction:

The number will be written as scientific notation when a number between 1 to10 is multiplied by a power of 10.

Answer to Problem 96A

  $\text{8}\text{.3}\times {\text{10}}^{-2}\text{ g}$

Explanation of Solution

  $0.0830\text{g}\text{= 8}\text{.3}\times {\text{10}}^{-2}\text{ g}$

The $0.0830\text{g}$ in scientific notion is $\text{8}\text{.3}\times {\text{10}}^{-2}\text{ g}$ .

(d)

Interpretation Introduction

Interpretation: The given measurement $9700000\text{ng}$ in scientific notation.

Concept introduction:

The number will be written as scientific notation when a number between 1 to10 is multiplied by a power of 10.

Answer to Problem 96A

  $9.7\times {10}^{-3}\text{g }$

Explanation of Solution

  $\begin{array}{c}9700000\text{ng}\text{= }9.7\times {10}^6\times {10}^{-9}\text{g}\\ \text{= }9.7\times {10}^{-3}\text{g }\left(\because 1\text{ng}=1\times {10}^{-9}\text{g}\right)\end{array}$

The $9700000\text{ng}$ in scientific notion is $9.7\times {10}^{-3}\text{g }$ .