Chapter 2.3, Problem 38PP

(a)

Interpretation Introduction

Interpretation:

The number $\text{84, 791}\text{kg}$ 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 38PP

$\text{84, 791}\text{kg}$ to four significant figures is $\text{84, 790}\text{kg}$.

Explanation of Solution

In the given number, $\text{84, 791}\text{kg}$ the fifth digit is less than 5, remove all the digits to the right and to the right to make the number up to four significant figures. The last zero in the final answer is not significant but if there were a decimal point after the zero than the last zero will be considered a significant figure.

$\text{84, 791}\text{kg}\text{=}\text{84, 790}\text{kg}$

(b)

Interpretation Introduction

Interpretation:

The given number $\text{38}\text{.5432}\text{g}$ 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 38PP

$\text{38}\text{.5432}\text{g}$ to four significant figures is $\text{38}\text{.54}\text{g}$.

Explanation of Solution

In the given number, $\text{38}\text{.5432}\text{g}$ the third digit after the decimal point is less than 5, then remove all the digits to the right to make the number up to four significant figures.

$\text{38}\text{.5432}\text{g}\text{=}\text{38}\text{.54}\text{g}$

(c)

Interpretation Introduction

Interpretation:

The given number $\text{256}\text{.75}\text{cm}$ 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 38PP

$\text{256}\text{.75}\text{cm}$ to four significant figures is $\text{256}\text{.8}\text{cm}$.

Explanation of Solution

In the given number, $\text{256}\text{.75}\text{cm}$ the second digit after the decimal point is equal to 5, add 1 to the digit in the previous place and then remove all the digits to the right to make the number up to four significant figures.

$\text{256}\text{.75}\text{cm}\text{=}\text{256}\text{.8}\text{cm}$

(d)

Interpretation Introduction

Interpretation:

The given number $\text{4}\text{.9356}\text{m}$ 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 38PP

$\text{4}\text{.9356}\text{m}$ to four significant figures is $\text{4}\text{.936}\text{m}$.

Explanation of Solution

In the given number, $\text{4}\text{.9356}\text{m}$ the fourth digit after the decimal point is greater than 5, add 1 to the digit in the previous place and then remove all the digits to the right to make the number up to four significant figures.

$\text{4}\text{.9356}\text{m}\text{=}\text{4}\text{.936}\text{m}$