Chapter 1, Problem 1.87QP

(a)

Interpretation Introduction

Interpretation:

The given number $\text{12}\text{.3}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Scientific notation:

It is a method used to write the large numbers or very small numbers sing the powers of ten.  The scientific notation is given as

  $\begin{array}{l}\text{N}\text{×}{\text{10}}^{\text{a}}\\ \text{where,}\text{N}\text{=}\text{any}\text{number}\\ \text{a}\text{=}\text{positive}\text{or}\text{negative}\text{integer}\end{array}$

Explanation of Solution

The given number is $\text{12}\text{.3}$.

To give the scientific notation, the decimal point is moved one place to the left.  So, the value of “a” will be positive.

  $\text{12}\text{.3}\text{=}\text{1}\text{.23}\text{×}{\text{10}}^{\text{1}}$

(b)

Interpretation Introduction

Interpretation:

The given number $\text{0}\text{.0569}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{0}\text{.0569}$.

To give the scientific notation, the decimal point is moved two places to the right to remove the zeros.  So, the value of “a” will be negative.

  $\text{0}\text{.0569}\text{=}\text{5}\text{.69}\text{×}\frac{\text{1}}{\text{100}}\text{=}\text{5}\text{.69}\text{×}{\text{10}}^{\text{-2}}$

(c)

Interpretation Introduction

Interpretation:

The given number $\text{-1527}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{-1527}$.

To give the scientific notation, the decimal point is moved three places to the left.  So, the value of “a” will be positive.

  $\text{-1527}\text{=}\text{-1}\text{.527}\text{×}\frac{\text{1}}{\text{1000}}\text{=}\text{-1}\text{.527}\text{×}{\text{10}}^{\text{3}}$

(d)

Interpretation Introduction

Interpretation:

The given number $\text{0}\text{.000000789}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{0}\text{.000000789}$.

To give the scientific notation, the decimal point is moved seven places to the right to remove the zeros.  So, the value of “a” will be negative.

  $\text{0}\text{.000000789}\text{=}\text{7}\text{.89}\text{×}{\text{10}}^{\text{-7}}$

(e)

Interpretation Introduction

Interpretation:

The given number $\text{92,000,000}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{92,000,000}$.

To give the scientific notation, the decimal point is moved seven places to the left.  So, the value of “a” will be positive.

  $\text{92,000,000}\text{=}\text{9}\text{.2}\text{×}{\text{10}}^{\text{7}}$

(f)

Interpretation Introduction

Interpretation:

The given number $\text{0}\text{.005280}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{0}\text{.005280}$.

To give the scientific notation, the decimal point is moved three places to the right.  So, the value of “a” will be negative.

  $\text{0}\text{.005280}\text{=}\text{5}\text{.280}\text{×}\frac{\text{1}}{\text{1000}}\text{=}\text{5}\text{.280}\text{×}{\text{10}}^{\text{-3}}$

(g)

Interpretation Introduction

Interpretation:

The given number $\text{1}\text{.279}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{1}\text{.279}$.

The scientific notation of the given number is

  $\text{1}\text{.279}\text{=}\text{1}\text{.279}\text{×}{\text{10}}^{\text{0}}$

(h)

Interpretation Introduction

Interpretation:

The given number $\text{-531}\text{.77}$ has to be expressed in scientific notation using the proper number of significant figures.

Concept Introduction:

Refer to part (a).

Explanation of Solution

The given number is $\text{-531}\text{.77}$.

To give the scientific notation, the decimal point is moved two places to the left.  So, the value of “a” will be positive.

  $\text{-531}\text{.77}\text{=}\text{-5}\text{.3177}\text{×}{\text{10}}^{\text{2}}$