Chapter 2, Problem 76A

(a)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.0045834}\text{mm}$ needs to be converted to scientific notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 76A

The scientific notation of the $\text{0}\text{.0045834}\text{mm}$ is $\text{4}\text{.5834}\times {10}^{-3}\text{mm}$.

Explanation of Solution

To convert $\text{0}\text{.0045834}\text{mm}$ to scientific notation, move the decimal point to the three places to the right side. Then the exponent will become negative three as the decimal point is moved to the right. Hence, the scientific notation of the $\text{0}\text{.0045834}\text{mm}$ is $\text{4}\text{.5834}\times {10}^{-3}\text{mm}$.

(b)

Interpretation Introduction

Interpretation:

The given number $\text{0}\text{.03054}\text{g}$ needs to be written in scientific notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 76A

The scientific notation of the $\text{0}\text{.03054}\text{g}$ is $\text{3}\text{.054}\times {10}^{-2}\text{g}$.

Explanation of Solution

To convert $\text{0}\text{.03054}\text{g}$ to scientific notation, move the decimal point to the two places to the right side. Then the exponent will become negative two as the decimal point is moved to the right. Hence, the scientific notation of the $\text{0}\text{.03054}\text{g}$ is $\text{3}\text{.054}\times {10}^{-2}\text{g}$.

(c)

Interpretation Introduction

Interpretation:

The number $\text{438, 904}\text{s}$ needs to be written in scientific notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 76A

The scientific notation of the $\text{438, 904}\text{s}$ is $\text{4}\text{.38904}\times {10}^5\text{s}$.

Explanation of Solution

To convert $\text{438, 904}\text{s}$ to scientific notation, move the decimal point to the five places to the left side. Then the exponent will become positive five as the decimal point is moved to the left. Hence, the scientific notation of the $\text{438, 904}\text{s}$ is $\text{4}\text{.38904}\times {10}^5\text{s}$.

(d)

Interpretation Introduction

Interpretation:

The number $\text{7, 004, 300, 000}\text{g}$ needs to be written in scientific notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Answer to Problem 76A

The scientific notation of the $\text{7, 004, 300, 000}\text{g}$ is $\text{7}\text{.0043}\times {10}^9\text{g}$.

Explanation of Solution

To convert $\text{7, 004, 300, 000}\text{g}$ to scientific notation, move the decimal point to the nine places to the left side. Then the exponent will become positive nine as the decimal point is moved to the left. Hence, the scientific notation of the $\text{7, 004, 300, 000}\text{g}$ is $\text{7}\text{.0043}\times {10}^9\text{g}$.