Chapter 2, Problem 77A

(a)

Interpretation Introduction

Interpretation:

The given number $\text{8}{\text{.348×10}}^{\text{6}}\text{km}$ needs to be written in ordinary notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ multiplied by $10$ raised to a power while the ordinary notation does not express the number as $10$ raised to an exponent rather the numbers are fully written with no arithmetic involved.

Answer to Problem 77A

The ordinary notation of $\text{8}{\text{.348×10}}^{\text{6}}\text{km}$ is $\text{8, 348, 000}\text{km}$.

Explanation of Solution

To convert $\text{8}{\text{.348×10}}^{\text{6}}\text{km}$ to ordinary notation, move the decimal point to the six places to the right side. The decimal point is moved to the right side because the exponent value is positive and the number represents the position of the decimal point needs to be moved. Hence, the ordinary notation of the $\text{8}{\text{.348×10}}^{\text{6}}\text{km}$ is $\text{8, 348, 000}\text{km}$.

(b)

Interpretation Introduction

Interpretation:

The given number $\text{3}{\text{.402×10}}^3\text{g}$ needs to be written in ordinary notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ multiplied by $10$ raised to a power while the ordinary notation does not express the number as $10$ raised to an exponent rather the numbers are fully written with no arithmetic involved.

Answer to Problem 77A

The scientific notation of the $\text{3}{\text{.402×10}}^3\text{g}$ is $\text{3, 402}\text{g}$.

Explanation of Solution

To convert $\text{3}{\text{.402×10}}^3\text{g}$ to ordinary notation, move the decimal point to the three places to the right side. The decimal point is moved to the right side because the exponent value is positive and the number represents the position of the decimal point needs to be moved. Hence, the ordinary notation of the $\text{3}{\text{.402×10}}^3\text{g}$ is $\text{3, 402}\text{g}$.

(c)

Interpretation Introduction

Interpretation:

The given number $\text{7}{\text{.6352×10}}^{-3}\text{kg}$ needs to be written in ordinary notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ multiplied by $10$ raised to a power while the ordinary notation does not express the number as $10$ raised to an exponent rather the numbers are fully written with no arithmetic involved.

Answer to Problem 77A

The scientific notation of the $\text{7}{\text{.6352×10}}^{-3}\text{kg}$ is $\text{0}\text{.0076352}\text{kg}$.

Explanation of Solution

To convert $\text{7}{\text{.6352×10}}^{-3}\text{kg}$ to ordinary notation, move the decimal point to the three places to the left side. The decimal point is moved to the left side because the exponent value is negative and the number represents the position of the decimal point needs to be moved. Hence, the ordinary notation of the $\text{7}{\text{.6352×10}}^{-3}\text{kg}$ is $\text{0}\text{.0076352}\text{kg}$.

(d)

Interpretation Introduction

Interpretation:

The given number $\text{3}{\text{.02×10}}^{-5}\text{s}$ needs to be written in ordinary notation.

Concept introduction:

Scientific notation is a term used to express any number as a number between $1$ and $10$ multiplied by $10$ raised to a power while the ordinary notation does not express the number as $10$ raised to an exponent rather the numbers are fully written with no arithmetic involved.

Answer to Problem 77A

The ordinary notation of $\text{3}{\text{.02×10}}^{-5}\text{s}$ is $\text{0}\text{.0000302}\text{s}$.

Explanation of Solution

To convert $\text{3}{\text{.02×10}}^{-5}\text{s}$ to ordinary notation, move the decimal point to the five places to the left side. The decimal point is moved to the left side because the exponent value is negative and the number represents the position of the decimal point needs to be moved. Hence, the ordinary notation of the $\text{3}{\text{.02×10}}^{-5}\text{s}$ is $\text{0}\text{.0000302}\text{s}$.