Chapter 5, Problem 69A

(a)

Interpretation Introduction

Interpretation:

The decimal point must be moved to express the numbers in standard scientific notation is to be determined as well as the exponent part will be positive, negative or zero, it should be checked also.

Concept Introduction :

A scientific notation for a positive integer always follows the given notation,

  $a\times {10}^b$

In the scientific notation, the large number is written in a small decimal form which is multiplied by the factor of power of 10 while in the case of the number that is less than one, the power of 10 has negative exponent and for that number which is larger than one, the power either is zero or positive.

Answer to Problem 69A

The given number is written in scientific notation like as, $5.5651\times {10}^4$ .

Explanation of Solution

For finding the $a$ :

Consider the number and move the decimal place to the right one position, such that

The given number is,

  $55651$

The new number is,

  $5.5651\times {10}^4$

For finding the $b$ :

The number of digits to the right of the decimal is counted, which is four

So, use these values in the above notation, and the resulted number is,

  $5.5651\times {10}^4$

(b)

Interpretation Introduction

Interpretation:

The decimal point must be moved to express the numbers in standard scientific notation is to be determined as well as the exponent part will be positive, negative or zero, it should be checked also.

Concept Introduction :

A scientific notation for a positive integer always follows the given notation,

  $a\times {10}^b$

In the scientific notation, the large number is written in small decimal form which is multiplied by the factor of power of 10 while in the case of the number that is less than one, the power of 10 has negative exponent and for that number which is larger than one, the power either is zero or positive.

Answer to Problem 69A

The given number is written in scientific notation like as, $8.991\times {10}^{-6}$ .

Explanation of Solution

For finding the $a$ :

Consider the number and move the decimal place to the right one position, such that

The given number is,

  $0.000008991$

The new number is,

  $8.991$

For finding the $b$ :

Here the number is less than one. Therefore, the power of 10 has negative exponent which is six.

So, the new number is,

  $8.991\times {10}^{-6}$

(c)

Interpretation Introduction

Interpretation:

The decimal point must be moved to express the numbers in standard scientific notation is to be determined as well as the exponent part will be positive, negative or zero, it should be checked also.

Concept Introduction : A scientific notation for a positive integer always follows the given notation,

  $a\times {10}^b$

In the scientific notation, the large number is written in small decimal form which is multiplied by the factor of power of 10 while in the case of the number that is less than one, the power of 10 has negative exponent and for that number which is larger than one, the power either is zero or positive.

Answer to Problem 69A

The given number is written in scientific notation like as, $2.04\times {10}^0$ .

Explanation of Solution

This number is already in scientific notation. Here, the power of 10 in exponent part is zero which means the exponent part is one.

(d)

Interpretation Introduction

Interpretation:

The decimal point must be moved to express the numbers in standard scientific notation is to be determined as well as the exponent part will be positive, negative or zero, it should be checked also.

Concept Introduction :

A scientific notation for a positive integer always follows the given notation,

  $a\times {10}^b$

In the scientific notation, the large number is written in small decimal form which is multiplied by the factor of power of 10 while in the case of the number that is less than one, the power of 10 has negative exponent and for that number which is larger than one, the power either is zero or positive.

Answer to Problem 69A

The given number is written in scientific notation like as, $8.83541\times {10}^5$ .

Explanation of Solution

For finding the $a$ :

Consider the number and move the decimal place to the right one position, such that

The given number is,

  $883541$

The new number is,

  $8.83541\times {10}^5$

For finding the $b$ :

The number of digits to the right of the decimal is counted, which is five.

So, use these values in the above notation, and the resulted number is,

  $8.83541\times {10}^5$

(e)

Interpretation Introduction

The decimal point must be moved to express the numbers in standard scientific notation is to be determined as well as the exponent part will be positive, negative or zero, it should be checked also.

Interpretation:

Concept Introduction :

A scientific notation for a positive integer always follows the given notation,

  $a\times {10}^b$

In the scientific notation, the large number is written in small decimal form which is multiplied by the factor of power of 10 while in the case of the number that is less than one, the power of 10 has negative exponent and for that number which is larger than one, the power either is zero or positive.

Answer to Problem 69A

The given number is written in scientific notation like as, $9.814\times {10}^{-2}$ .

Explanation of Solution

For finding the $a$ :

Consider the number and move the decimal place to the right one position, such that

The given number is,

  $0.09814$

The new number is,

  $9.814$

For finding the $b$ :

Here the number is less than one. Therefore, the power of 10 has negative exponent which is two

So, the new number is,

  $9.814\times {10}^{-2}$