Chapter 2, Problem 110A

(a)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.003210}\text{g}$ needs to be rounded off to three 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 110A

$\text{0}\text{.003210}\text{g}$ is rounded off to three significant figure is $\text{0}\text{.00321}\text{g}$

Explanation of Solution

Take off the zero at the end of the former number to round off $\text{0}\text{.003210}\text{g}$ to three significant figures. Hence, the value will be $\text{0}\text{.00321}\text{g}$.

(b)

Interpretation Introduction

Interpretation:

The number $\text{3}\text{.8754}\text{kg}$ needs to be rounded off to three 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 110A

$\text{3}\text{.8754}\text{kg}$ is rounded off to three significant figure is $\text{3}\text{.88}\text{kg}$.

Explanation of Solution

Take off 5 and 4 digits at the end of the former number to round off $\text{3}\text{.8754}\text{kg}$ to three significant figures. Hence, the value will be $\text{3}\text{.88}\text{kg}$.

(c)

Interpretation Introduction

Interpretation:

The number $\text{219, 034}\text{m}$ needsto be rounded off to three 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 110A

$\text{219, 034}\text{m}$ is rounded off to three significant figure is $\text{219, 000}\text{m}$.

Explanation of Solution

Take off the digits 3 and 4 at the end of the former number with zero to round off $\text{219, 034}\text{m}$ to three significant figures. Hence, the value will be $\text{219, 000}\text{m}$.

(d)

Interpretation Introduction

Interpretation:

The number $\text{25}\text{.38}\text{L}$ needs to be rounded off to three 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 110A

$\text{25}\text{.38}\text{L}$ is rounded off to three significant figure is $\text{25}\text{.4}\text{L}$.

Explanation of Solution

Take off the 8 at the end of the number $\text{25}\text{.38}\text{L}$ and round off 3 to 4 (as 8 > 5) to three significant figures. Hence, the value will be $\text{25}\text{.4}\text{L}$.

(e)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.08763}\text{cm}$ needs to be rounded off to three 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 110A

$\text{0}\text{.08763}\text{cm}$ is rounded off to three significant figure is $\text{0}\text{.0876}\text{cm}$.

Explanation of Solution

Take off the digit 3 at the end of the number to round off $\text{0}\text{.08763}\text{cm}$ to three significant figures. Hence, the value will be $\text{0}\text{.0876}\text{cm}$.

(f)

Interpretation Introduction

Interpretation:

The number $\text{0}\text{.003109}\text{mg}$ needs to be rounded off to three 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 110A

$\text{0}\text{.003109}\text{mg}$ is rounded off to three significant figure is $\text{0}\text{.00311}\text{mg}$.

Explanation of Solution

Take off the 9 at the end of the number $\text{0}\text{.003109}\text{mg}$ and round off zero to a 1 to three significant figures. Hence, the value will be $\text{0}\text{.00311}\text{mg}$.