Chapter 5, Problem 7A

(a)

Interpretation Introduction

Interpretation: The number $0.00883$ needs to be written in standard scientific notation.

Concept Introduction: The scientific notation is the simple way to rewrite the decimal number. It is used to write very large or very small numbers with multiplied by a power of 10.

Answer to Problem 7A

  $0.00883$ = $8.830\times {10}^{-3}$

Explanation of Solution

To convert ordinary number into scientific notation, the decimal point must move to the left of the first non-zero integer. The number of places the decimal point comes as the power of the exponent which represents as "power of 10".Thus, the standard scientific notation of $0.00883$ must be $8.830\times {10}^{-3}$ .

(b)

Interpretation Introduction

Interpretation: The number $86.29\times {10}^5$ needs to be written in standard scientific notation.

Concept Introduction: The scientific notation is the simple way to rewrite the decimal number. It is used to write very large or very small numbers with multiplied by a power of 10.

Answer to Problem 7A

  $86.29\times {10}^5$ = $8.629\times {10}^4$

Explanation of Solution

The given number changes such that decimal comes after first non-zero digit. The number of places the decimal point comes as the power of the exponent which represents as "power of 10". Thus, the standard scientific notation of $86.29\times {10}^5$ must be $8.629\times {10}^4$ .

(c)

Interpretation Introduction

Interpretation: The number $0.000393\times {10}^{-5}$ needs to be written in standard scientific notation.

Concept Introduction: The scientific notation is the simple way to rewrite the decimal number. It is used to write very large or very small numbers with multiplied by a power of 10.

Answer to Problem 7A

  $0.000393\times {10}^{-5}$ = $3.930\times {10}^{-8}$

Explanation of Solution

The given number is changes such that decimal comes after first non-zero digit. The number of places the decimal point comes as the power of the exponent which represents as "power of 10". Thus, the standard scientific notation of $0.000393\times {10}^{-5}$ must be $3.930\times {10}^{-8}$ .

(d)

Interpretation Introduction

Interpretation: The number $55380$ needs to be written in standard scientific notation.

Concept Introduction: The scientific notation is the simple way to rewrite the decimal number. It is used to write very large or very small numbers with multiplied by a power of 10.

Answer to Problem 7A

  $55380$ = $5.5380\times {10}^4$

Explanation of Solution

To convert ordinary number into scientific notation, the decimal point must move to the left of the first non-zero integer. The number of places the decimal point comes as the power of the exponent which represents as "power of 10". Thus, the standard scientific notation of $55380$ must be $5.5380\times {10}^4$ .

(e)

Interpretation Introduction

Interpretation: The number $6289.2$ needs to be written in standard scientific notation.

Concept Introduction: The scientific notation is the simple way to rewrite the decimal number. It is used to write very large or very small numbers with multiplied by a power of 10.

Answer to Problem 7A

  $6289.2$ = $6.289\times {10}^3$

Explanation of Solution

To convert ordinary number into scientific notation, the decimal point must move to the left of the first non-zero integer. The number of places the decimal point comes as the power of the exponent which represents as "power of 10". Thus, the standard scientific notation of $6289.2$ must be $6.289\times {10}^3$ .

(f)

Interpretation Introduction

Interpretation: The number $6.773\times {10}^3\times {10}^{-2}$ needs to be written in standard scientific notation.

Concept Introduction: The scientific notation is the simple way to rewrite the decimal number. It is used to write very large or very small numbers with multiplied by a power of 10.

Answer to Problem 7A

  $6.773\times {10}^3\times {10}^{-2}$ = $67.73=6.773\times {10}^1$

Explanation of Solution

The given number is $6.773\times {10}^3\times {10}^{-2}$ .

Here, power of 10 gets added and number becomes 67.73. To convert ordinary number into scientific notation, the decimal point must move to the left of the first non-zero integer. The number of places the decimal point comes as the power of the exponent which represents as "power of 10". Thus, the standard scientific notation of $6.773\times {10}^3\times {10}^{-2}$ must be $67.73=6.773\times {10}^1$ .