Chapter 2, Problem 91A

(a)

Interpretation Introduction

Interpretation:

The number $\text{431, 801}\text{kg}$ needs to be round off to four significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 91A

$\text{431, 801}\text{kg}$ is rounded off to four significant figure is $\text{431, 800}\text{kg}$.

Explanation of Solution

To round off the given number $\text{431, 801}\text{kg}$ to four significant figures, replace the last digit $1$ with zero. Then, the number with four significant figures is $\text{431, 800}\text{kg}$.

(b)

Interpretation Introduction

Interpretation:

The number $\text{10, 235}\text{.0}\text{mg}$ needs to be rounded off to four significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 91A

$\text{10, 235}\text{.0}\text{mg}$ is rounded off to four significant figure is $\text{10, 240}\text{mg}$.

Explanation of Solution

To round off given number $\text{10, 235}\text{.0}\text{mg}$ to four significant figures, replace the fourth digit $3$ with $4$.

Get rid of decimal point and delete all the numbers after that. Then, the number with four significant figures is $\text{10, 240}\text{mg}$.

(c)

Interpretation Introduction

Interpretation:

The number $\text{1}\text{.0348}\text{m}$ needs to be rounded off to four significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 91A

$\text{1}\text{.0348}\text{m}$ is rounded off to four significant figure is $\text{1}\text{.035}\text{m}$.

Explanation of Solution

To round off the given number $\text{1}\text{.0348}\text{m}$ to four significant figures, replace the last digit $4$ with $5$ as the fifth digit is greater than 5. Then, the number with four significant figures is $\text{1}\text{.035}\text{m}$.

(d)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.004384010}\text{cm}$ needs to be rounded off to four significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 91A

$\text{0}\text{.004384010}\text{cm}$ is rounded off to four significant figure is $\text{0}\text{.004384}\text{cm}$.

Explanation of Solution

To round off the given number $\text{0}\text{.004384010}\text{cm}$ to four significant figures, ignore the zeros at the starting and delete $1$ and two 0s at the end of the number. Then, the number with four significant figures is $\text{0}\text{.004384}\text{cm}$.

(e)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.00078100}\text{mL}$ needs to be rounded off to four significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 91A

$\text{0}\text{.00078100}\text{mL}$ is rounded off to four significant figure is $\text{0}\text{.0007810}\text{mL}$.

Explanation of Solution

To round off the given number $\text{0}\text{.00078100}\text{mL}$ to four significant figures, ignore the zeros at the starting and delete only one zero at the end of the number. Then, the number with four significant figures is $\text{0}\text{.0007810}\text{mL}$.

(f)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.0098641}\text{cg}$ needs to be rounded off to four significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 91A

$\text{0}\text{.0098641}\text{cg}$ is rounded off to four significant figure is $\text{0}\text{.009864}\text{cg}$.

Explanation of Solution

To round off the given number $\text{0}\text{.0098641}\text{cg}$ to four significant figures, ignore the zeros at the starting and delete $1$ at the end of the number. Then, the number with four significant figures is $\text{0}\text{.009864}\text{cg}$.