Chapter 2.3, Problem 35PP

(a)

Interpretation Introduction

Interpretation:

The number of significant figure in $\text{508}\text{.0}\text{L}$ needs to be determined.

Concept introduction:

The term significant figures can be defined as the total number of digits including the last digit whose value is undecided. There are following rules are for the determination of significant figures as follows:

• All the non-zero and zero digits between non-zero digits are considered to be significant.
• Zeros to the left of the first non-zero digits in any number are not significant.
• If any number ends in zeros which are right of a decimal point, then the zeros are considered to be significant.
• If any number ends in zeros which are not to the right of a decimal point, then the zeros may or may not be significant.

Answer to Problem 35PP

The number of significant figures in $\text{508}\text{.0}\text{L}$ is four.

Explanation of Solution

The number of significant figures in $\text{508}\text{.0}\text{L}$ contains four significant figures because the zero which is right of a decimal point, then the zero is considered to be significant. Hence, the given number contains four significant figures.

(b)

Interpretation Introduction

Interpretation:

The number of significant figures in $\text{1}\text{.0200}\times {\text{10}}^5\text{kg}$ needs to be determined.

Concept introduction:

The term significant figures can be defined as the total number of digits including the last digit whose value is undecided. There are following rules are for the determination of significant figures as follows:

• All the non-zero and zero digits between non-zero digits are considered to be significant.
• Zeros to the left of the first non-zero digits in any number are not significant.
• If any number ends in zeros which are right of a decimal point, then the zeros are considered to be significant.
• If any number ends in zeros which are not to the right of a decimal point, then the zeros may or may not be significant.

Answer to Problem 35PP

The number of significant figures in $\text{1}\text{.0200}\times {\text{10}}^5\text{kg}$ is five.

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. There are five significant figures in the given number. All the zeros in the given number are significant.

(c)

Interpretation Introduction

Interpretation:

The number of significant figures in $820,400.0\text{L}$ needs to be determined.

Concept introduction:

The term significant figures can be defined as the total number of digits including the last digit whose value is undecided. There are following rules are for the determination of significant figures as follows:

• All the non-zero and zero digits between non-zero digits are considered to be significant.
• Zeros to the left of the first non-zero digits in any number are not significant.
• If any number ends in zeros which are right of a decimal point, then the zeros are considered to be significant.
• If any number ends in zeros which are not to the right of a decimal point, then the zeros may or may not be significant.

Answer to Problem 35PP

The number of significant figures in $820,400.0\text{L}$ is seven.

Explanation of Solution

The number of significant figures in $820,400.0\text{L}$ contains seven significant figures because the last zero after the decimal point is considered to be significant. Hence, the given number contains seven significant figures.

(d)

Interpretation Introduction

Interpretation:

The number of significant figures in $\text{807, 000}\text{kg}$ needs to be determined.

Concept introduction:

The term significant figures can be defined as the total number of digits including the last digit whose value is undecided. There are following rules are for the determination of significant figures as follows:

• All the non-zero and zero digits between non-zero digits are considered to be significant.
• Zeros to the left of the first non-zero digits in any number are not significant.
• If any number ends in zeros which are right of a decimal point, then the zeros are considered to be significant.
• If any number ends in zeros which are not to the right of a decimal point, then the zeros may or may not be significant.

Answer to Problem 35PP

The number of significant figures in $\text{807, 000}\text{kg}$ is six.

Explanation of Solution

The number of significant figures in $\text{807, 000}\text{kg}$ contains six significant figures because the last three zeros are considered to be significant. Hence, the given number contains six significant figures.