Chapter 1, Problem 1.57P

(a)

Interpretation Introduction

Interpretation:

The number $282.0$ is to be written in scientific notation.

Concept introduction:

Scientific notations are used to express the given large or small quantities in a compact way by making use of exponents.

The general representation of scientific notation is,

$N\times {10}^{\text{a}}$

Here, $N$ is the number between 1 and 9, and $\text{a}$ is the integer.

The decimal point is shifted towards right or left such that only one nonzero digit is present to the left of the decimal point and the number of places the decimal point is shifted is expressed as the exponent power. If the decimal point is shifted towards right from its original place a negative exponent result and vice-versa.

(b)

Interpretation Introduction

Interpretation:

The number $0.0380$ is to be written in scientific notation.

Concept introduction:

Scientific notations are used to express the given large or small quantities in a compact way by making use of exponents.

The general representation of scientific notation is,

$N\times {10}^{\text{a}}$

Here, $N$ is the number between 1 and 9, and $\text{a}$ is the integer.

The decimal point is shifted towards right or left such that only one nonzero digit is present to the left of the decimal point and the number of places the decimal point is shifted is expressed as the exponent power. If the decimal point is shifted towards right from its original place a negative exponent result and vice-versa.

(c)

Interpretation Introduction

Interpretation:

The number $4270.8$ is to be written in scientific notation.

Concept introduction:

Scientific notations are used to express the given large or small quantities in a compact way by making use of exponents.

The general representation of scientific notation is,

$N\times {10}^{\text{a}}$

Here, $N$ is the number between 1 and 9, and $\text{a}$ is the integer.

The decimal point is shifted towards right or left such that only one nonzero digit is present to the left of the decimal point and the number of places the decimal point is shifted is expressed as the exponent power. If the decimal point is shifted towards right from its original place a negative exponent result and vice-versa.

(d)

Interpretation Introduction

Interpretation:

The number $58200.9$ is to be written in scientific notation.

Concept introduction:

Scientific notations are used to express the given large or small quantities in a compact way by making use of exponents.

The general representation of scientific notation is,

$N\times {10}^{\text{a}}$

Here, $N$ is the number between 1 and 9, and $\text{a}$ is the integer.

The decimal point is shifted towards right or left such that only one nonzero digit is present to the left of the decimal point and the number of places the decimal point is shifted is expressed as the exponent power. If the decimal point is shifted towards right from its original place a negative exponent result and vice-versa.