Chapter 2.3, Problem 39PP

(a)

Interpretation Introduction

Interpretation:

The given number $\text{0}\text{.00054818}\text{g}$ needs to be rounded off to four significant figures in scientific notation.

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 39PP

$\text{0}\text{.00054818}\text{g}$ to four significant figures in scientific notation is $5.482\times {\text{10}}^{-4}\text{g}$.

Explanation of Solution

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Here, 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.

$\begin{array}{c}\text{0}\text{.00054818}\text{g}\text{=}\text{5}\text{.4818}\times {\text{10}}^{-4}\text{g}\\ =5.482\times {\text{10}}^{-4}\text{g}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The given $\text{136, 758}\text{kg}$ needs to be rounded off to four significant figures in scientific notation.

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 39PP

$\text{136, 758}\text{kg}$ to four significant figures in scientific notation is $1.368\times {\text{10}}^5\text{kg}$.

Explanation of Solution

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Here, the fourth 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.

$\begin{array}{c}\text{136, 758}\text{kg}\text{=}\text{1}\text{.36758}\times {\text{10}}^5\text{kg}\\ =1.368\times {\text{10}}^5\text{kg}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The given number $\text{308, 659, 000}\text{mm}$ needs to be rounded off to four significant figures in scientific notation.

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 39PP

$\text{308, 659, 000}\text{mm}$ to four significant figures in scientific notation is $\text{3}\text{.087}\times {\text{10}}^8\text{mm}$.

Explanation of Solution

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Here, the fourth 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.

$\begin{array}{c}\text{308, 659, 000}\text{mm}\text{=}\text{308659}\times {\text{10}}^3\text{mm}\\ =\text{3}\text{.08659}\times {\text{10}}^8\text{mm}\\ \text{=}\text{3}\text{.087}\times {\text{10}}^8\text{mm}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The given number $\text{2}\text{.0145}\text{mL}$ needs to be rounded off to four significant figures in scientific notation.

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 39PP

$\text{2}\text{.0145}\text{mL}$ to four significant figures in scientific notation is $\text{20}\text{.15}\times {\text{10}}^{-1}\text{mL}$.

Explanation of Solution

Scientific notation is a term used to express any number as a number between $1$ and $10$ (termed as coefficient) multiplied by $10$ raised to a power (termed as exponent). Scientists express numbers in a scientific notation form.

Here, the third 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.

$\begin{array}{c}\text{2}\text{.0145}\text{mL}\text{=}\text{20}\text{.145}\times {\text{10}}^{-1}\text{mL}\\ \text{=}\text{20}\text{.15}\times {\text{10}}^{-1}\text{mL}\end{array}$