Chapter 2, Problem 79A

(a)

Interpretation Introduction

Interpretation:

The given multiplication problem needs to be represented in scientific notation.

$\left(4.8\times {10}^5\text{km}\right)\times \left(2.0\times {10}^3\text{km}\right)$

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 79A

The complete multiplication of the given problem is $\text{9}\text{.6}\times {10}^8{\text{km}}^2$.

Explanation of Solution

When multiplying the numbers in scientific notation, add the exponent values. Simply, multiply both numbers and add the exponent values.

$\begin{array}{c}\left(4.8\times {10}^5\text{km}\right)\times \left(2.0\times {10}^3\text{km}\right)=\left(4.8\times 2.0\right)\times {10}^{5+3}{\text{km}}^2\\ \text{=}\text{9}\text{.6}\times {10}^8{\text{km}}^2\end{array}$

(b)

Interpretation Introduction

Interpretation:

The given multiplication problem needs to be completed in scientific notation.

$\left(3.33\times {10}^{-4}\text{m}\right)\times \left(3.00\times {10}^{-5}\text{m}\right)$

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 79A

The complete multiplication of the given problem is $\text{9}\text{.99}\times {10}^{-9}{\text{m}}^2$.

Explanation of Solution

When multiplying the numbers in scientific notation, add the exponent values. Simply, multiply both numbers and add the exponent values.

$\begin{array}{c}\left(3.33\times {10}^{-4}\text{m}\right)\times \left(3.00\times {10}^{-5}\text{m}\right)=\left(3.33\times 3.00\right)\times {10}^{-4-5}{\text{m}}^2\\ \text{=}\text{9}\text{.99}\times {10}^{-9}{\text{m}}^2\end{array}$

(c)

Interpretation Introduction

Interpretation:

The given multiplication problem needs to be completed in scientific notation.

$\left(1.2\times {10}^6\text{m}\right)\times \left(1.5\times {10}^{-7}\text{m}\right)$

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 79A

The complete multiplication of the given problem is $1.8\times {10}^{-1}{\text{m}}^2$.

Explanation of Solution

When multiplying the numbers in scientific notation, add the exponent values. Simply, multiply both numbers and add the exponent values.

$\begin{array}{c}\left(1.2\times {10}^6\text{m}\right)\times \left(1.5\times {10}^{-7}\text{m}\right)=\left(1.2\times 1.5\right)\times {10}^{6-7}{\text{m}}^2\\ \text{=}1.8\times {10}^{-1}{\text{m}}^2\end{array}$

(d)

Interpretation Introduction

Interpretation:

The given division problem needs to be completed in scientific notation.

$\left(8.42\times {10}^8\text{kL}\right)÷\left(4.21\times {10}^3\text{kL}\right)$

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 79A

The complete division of the given problem is $\text{2}\text{.0}\times {10}^5$.

Explanation of Solution

When dividing the numbers in scientific notation, subtract the exponent values. Simply, divide both numbers and subtract the exponent values.

$\begin{array}{c}\left(8.42\times {10}^8\text{kL}\right)÷\left(4.21\times {10}^3\text{kL}\right)=\left(8.42÷4.21\right)\times {10}^{8-3}\\ \text{=}\text{2}\text{.0}\times {10}^5\end{array}$

(e)

Interpretation Introduction

Interpretation:

The given division problem needs to be completed in scientific notation.

$\left(8.4\times {10}^6\text{L}\right)÷\left(2.4\times {10}^{-3}\text{L}\right)$

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 79A

The complete division of the given problem is $3.5\times {10}^9$.

Explanation of Solution

When dividing the numbers in scientific notation, subtract the exponent values. Simply, divide both numbers and subtract the exponent values.

$\begin{array}{c}\left(8.4\times {10}^6\text{L}\right)÷\left(2.4\times {10}^{-3}\text{L}\right)=\left(8.4÷2.4\right)\times {10}^{6-\left(-3\right)}\\ =\left(8.4÷2.4\right)\times {10}^{6+3}\\ \text{=}3.5\times {10}^9\end{array}$

(f)

Interpretation Introduction

Interpretation:

The given division problem needs to be converted in scientific notation.

$\left(3.3\times {10}^{-4}\text{mL}\right)÷\left(1.1\times {10}^{-6}\text{mL}\right)$

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 79A

The complete division of the given problem is $3.0\times {10}^2$.

Explanation of Solution

When dividing the numbers in scientific notation, subtract the exponent values. Simply, divide both numbers and subtract the exponent values.

$\begin{array}{c}\left(3.3\times {10}^{-4}\text{mL}\right)÷\left(1.1\times {10}^{-6}\text{mL}\right)=\left(3.3÷1.1\right)\times {10}^{-4-\left(-6\right)}\\ =\left(3.3÷1.1\right)\times {10}^{-4+6}\\ \text{=}3.0\times {10}^2\end{array}$